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This thesis aims to systematically unpack the relationship between financial development and income inequality using a broad panel dataset of up to 151 developed and developing countries for the period 1980 to 2014. The first empirical chapter (Chapter 4) investigates whether the finance-inequality nexus depends on the specific measure used to capture the multidimensional aspects of financial development - such as access, depth, efficiency, and stability - related to banking systems and stock markets. Using a series of panel data techniques with various robustness checks, one of the significant findings to emerge from this study is that while some aspects of financial development contribute towards alleviating income inequality, others may have a reverse impact. To further unpack the finance-inequality nexus, the second empirical chapter (Chapter 5) probes beyond the mean effects to explore whether the effect of financial development on income inequality varies according to the level of inequality. For this purpose, a quantile regressions technique is adopted to ascertain the full distributional impact of financial development pertaining to not only the centre but also the upper and lower ends of the inequality spectrum. The results reveal that different aspects of financial development may not yield the same effect for countries with higher inequality levels compared to countries with lower inequality. Furthermore, these findings shed meaningful light on which aspects of banking systems and stock markets aggravate or alleviate income inequality in the context of countries with high-, moderate- or low-income inequality, thereby aiding policymakers to devise and implement effectual policy decisions. Finally, the third empirical chapter (Chapter 6) aims to unfold whether the relationship between financial development and inequality is contingent on the degree of financial development. While existing theory suggests that the impact of financial development on inequality may depend on the stage of financial development that the country is undergoing (Greenwood and Jovanovic, 1990; Aghion and Bolton, 1997), the empirical studies on such regime-shifting effects have remained relatively scant. This chapter, therefore, investigates the implications of financial regimes in exerting a differential impact on income distribution. To this end, a panel threshold regression approach is employed, which allows the detection and inferential analyses of possible threshold effects and regime shifts in economic relationships. The key finding is that the finance-inequality nexus is indeed contingent on the distinct level or regime of financial development. Therefore, the findings of this thesis collectively provide several critical insights on the finance-inequality nexus. The important lesson to be learned is that researchers should not simply rely on a narrow definition of financial development to ascertain the impact on income inequality. At the same time, policymakers need to be more cautious in their approach towards effectively targeting and promoting the inequality-reducing aspects of financial development in the context of countries with different inequality levels and financial regimes.

Background: The consequences of poor nutrition are well known and of wide concern. Governments and public health agencies utilise food and diet surveillance data to make decisions that lead to improvements in nutrition. These surveys often utilise complex sample designs for efficient data collection. There are several challenges in the statistical analysis of dietary intake data collected using complex survey designs, which have not been fully addressed by current methods. Firstly, the shape of the distribution of intake can be highly skewed due to the presence of outlier observations and a large proportion of zero observations arising from the inability of the food diary to capture consumption within the period of observation. Secondly, dietary data is subject to variability arising from day-to-day individual variation in food consumption and measurement error, to be accounted for in the estimation procedure for correct inferences. Thirdly, the complex sample design needs to be incorporated into the estimation procedure to allow extrapolation of results into the target population. This thesis aims to develop novel statistical methods to address these challenges, applied to the analysis of iron intake data from the UK National Diet and Nutrition Survey Rolling Programme (NDNS RP) and UK national prescription data of iron deficiency medication. Methods: 1) To assess the nutritional status of particular population groups a two-part model with a generalised gamma (GG) distribution was developed for intakes that show high frequencies of zero observations. The two-part model accommodated the sources of data variation of dietary intake with a random intercept in each component, which could be correlated to allow a correlation between the probability of consuming and the amount consumed. 2) To identify population groups at risk of low nutrient intakes, a linear quantile mixed-effects model was developed to model quantiles of the distribution of intake as a function of explanatory variables. The proposed approach was illustrated by comparing the quantiles of iron intake with Lower Reference Nutrient Intakes (LRNI) recommendations using NDNS RP. This thesis extended the estimation procedures of both the two-part model with GG distribution and the linear quantile mixed-effects model to incorporate the complex sample design in three steps: the likelihood function was multiplied by the sample weightings; bootstrap methods for the estimation of the variance and finally, the variance estimation of the model parameters was stratified by the survey strata. 3) To evaluate the allocation of resources to alleviate nutritional deficiencies, a quantile linear mixed-effects model was used to analyse the distribution of expenditure on iron deficiency medication across health boards in the UK. Expenditure is likely to depend on the iron status of the region; therefore, for a fair comparison among health boards, iron status was estimated using the method developed in objective 2) and used in the specification of the median amount spent. Each health board is formed by a set of general practices (GPs), therefore, a random intercept was used to induce correlation between expenditure from two GPs from the same health board. Finally, the approaches in objectives 1) and 2) were compared with the traditional approach based on weighted linear regression modelling used in the NDNS RP reports. All analyses were implemented using SAS and R. Results: The two-part model with GG distribution fitted to amount of iron consumed from selected episodically food, showed that females tended to have greater odds of consuming iron from foods but consumed smaller amounts. As age groups increased, consumption tended to increase relative to the reference group though odds of consumption varied. Iron consumption also appeared to be dependent on National Statistics Socio-Economic Classification (NSSEC) group with lower social groups consuming less, in general. The quantiles of iron intake estimated using the linear quantile mixed-effects model showed that more than 25% of females aged 11-50y are below the LRNI, and that 11-18y girls are the group at highest of deficiency in the UK. Predictions of spending on iron medication in the UK based on the linear quantile mixed-effects model showed areas of higher iron intake resulted in lower spending on treating iron deficiency. In a geographical display of expenditure, Northern Ireland featured the lowest amount spent. Comparing the results from the methods proposed here showed that using the traditional approach based on weighted regression analysis could result in spurious associations. Discussion: This thesis developed novel approaches to the analysis of dietary complex survey data to address three important objectives of diet surveillance, namely the mean estimation of food intake by population groups, identification of groups at high risk of nutrient deficiency and allocation of resources to alleviate nutrient deficiencies. The methods provided models of good fit to dietary data, accounted for the sources of data variability and extended the estimation procedures to incorporate the complex sample survey design. The use of a GG distribution for modelling intake is an important improvement over existing methods, as it includes many distributions with different shapes and its domain takes non-negative values. The two-part model accommodated the sources of data variation of dietary intake with a random intercept in each component, which could be correlated to allow a correlation between the probability of consuming and the amount consumed. This also improves existing approaches that assume a zero correlation. The linear quantile mixed-effects model utilises the asymmetric Laplace distribution which can also accommodate many different distributional shapes, and likelihood-based estimation is robust to model misspecification. This method is an important improvement over existing methods used in nutritional research as it explicitly models the quantiles in terms of explanatory variables using a novel quantile regression model with random effects. The application of these models to UK national data confirmed the association of poorer diets and lower social class, identified the group of 11-50y females as a group at high risk of iron deficiency, and highlighted Northern Ireland as the region with the lowest expenditure on iron prescriptions.

This thesis contributes to the field of economics of happiness by examining, for the first time in detail, the determinants of subjective well-being (SWB) in Macedonia. Three data sources, European Quality of Life Survey, World Bank Indicators and World Governance Indicators for the periods 2007–2008 and 2011–2012 are analysed, by using Ordinary Least Squares, ordered probit, quantile regression models, Shapley decompositions, statistical kernel matching and Blinder-Oaxaca decompositions, which support the development of three different but related empirical studies. The first study analyses the impact of a range of socio-economic characteristics. The results suggest that employment activity, health and household income are the most prominent individual-level determinants of SWB in Macedonia. The second study focuses on the labour market, especially those factors related to employment or unemployment status and finds that job insecurity, duration of unemployment and the receipt of unemployment benefits negatively affect the SWB of Macedonians. The last study places Macedonia in a broader European context and finds that institutional factors (such as corruption and social trust) and macro-economic conditions (unemployment and GDP) can help to explain the differences in SWB between Macedonia and other countries in Europe. The analysis also sheds lights on the rise in SWB in Macedonia, and finds that this increase is only partly related to differences in personal characteristics, which suggests that the data are unable to explain some of the rise in SWB. Possible reasons are suggested for this. The main policy implications are that the key areas for intervention in Macedonia to further enhance SWB are labour-market issues (employment and income levels) as well as institutional reforms.

This thesis describes research relating to data analysis for improved risk assessment in buried pipelines. The kind of pipelines being considered includes onshore underground pipelines. External corrosion in buried pipelines is often complex to understand due to the diversity of factors affecting the corrosion process and in many cases, these pipelines operate in hostile environments. They may be less susceptible to failure and their failure may have different consequences in relation to aboveground pipelines. However, there is a limitation with respect what inspection techniques are efficient and therefore the assessment process is more difficult to be carried out. One of the major integrity risks to aging pipelines is the degradation and failure of the protective coating, leading to external corrosion. A commonly used approach for the assessment of external corrosion risk of buried pipelines is based on measurements from indirect inspections which are used to assess the likelihood of external corrosion. The underlying assumption is that indirect measurements can provide data to reliably identify corrosion defects on the pipeline, and prioritise defects according to their risk to pipeline integrity. One established method to determine the condition of the pipeline coating is to use an above-ground technique, such as DCVG, to locate the severity of the any coating defects, that may be present on a pipeline. Whilst the location aspect of this technique is very accurate and reliable, the severity may not correlate very well with the actual size of the coating defect when examined after excavation. Therefore, there is a need to refine the coating defect sizing model to provide a better indication of the severity of coating defects. However, there is little available research carried out to investigate this in a systematic manner. A further area of uncertainty relates to the correlation between the indirect inspection measurements, and the severity of the corrosion found following excavation. The development and refinement of regression models to address this link is required to ensure better corrosion predictions and improved inspection plans. The aim of the research described in this thesis is to analyse the external corrosion phenomenon in underground pipelines through the analysis of data from inspection reports and soil surveys. This aim has been achieved through specific studies at TWI, two of which are described in this thesis. The contribution to knowledge of the research included in this thesis is the improvement on the understanding of pipeline coating condition and external corrosion phenomenon in underground pipelines through the analysis of data from inspection reports and soil survey. Also, the identification of key factors affecting external corrosion along the probability distribution function, including factors that affect the initiation of corrosion and factors which have more importance in cases of severe corrosion. The novelty of the research herein presented relies in the application of quantile regression to pipeline data combined with soil properties which has never been applied before. The results improve the understanding of pipeline coating condition and external corrosion in underground pipelines. Also, it proposes suggestions for improving the interpretation of the NACE ECDA SP-0502 standard which may lead to significant savings in the pipeline industry.

This thesis is an attempt to bridge some research gaps in the area of behavioural finance and investment through adopting the three essays scheme of PhD dissertations. There is a widespread belief that the traditional finance theory failed to provide a sufficient and plausible explanation for (1) what motivates individual investors to trade, (2) the pattern of their trading and the formation of their portfolios, (3) the determinants of cross section of expected returns other than risk. Behavioural Finance, however, offers more realistic assumptions based on two building blocks; behavioural biases of irrational investors and the limits of arbitrage that prevent the arbitrageurs from correcting mispricing and pushing prices back to fundamental values. This dissertation is structured as follows: In the first essay, the disposition effect is defined as the propensity of investors to realize gains too early while being loath to realize losses. Capital gains overhang is a measure of unrealized capital gains and losses that is associated with the disposition effect and the trading activities of behaviourally biased investors. We discover that firm characteristics can play a role in explaining variations in the capital gains overhang that is consistent with the activities of behaviourally biased and disposition investors. Specifically, we find that capital gains overhang is increasing in firm attributes that attract behaviourally biased investors, namely, earnings per share, leverage, growth and size. Capital gains overhang is also declining in market liquidity, possibly because liquidity allows behaviourally biased investors to excessively trade shares and beta and corporate earnings, probably because when high risk and inefficient firms experience losses, disposition investors experience capital losses that they are reluctant to realize. In the second essay, quantile regressions are employed to analyse the relationship between the unrealized capital gains overhang and expected returns. The ability of the disposition effect to generate momentum is also considered for the extreme expected return regions (0.05th) and (0.95th) quantiles. To do so, 450,617 observations belonging to 5176 US firms are employed, covering a time span from January 1998 to June 2015. Following the methodology of Grinblatt and Han (2005), the findings show significant differences across various quantiles in terms of signs and magnitudes. These findings indicate a nonlinear relationship between capital gains overhang and expected returns since the impact of capital gains overhang as a proxy for disposition effect on expected returns vary across the expected return distribution. More precisely, the coefficients of capital gains overhang are significantly positive and decline as the expected returns quantiles increase from the lowest to the median expected return quantiles. However, they become significantly negative and rise with the increase in expected returns quantiles above median expected returns quantiles. The findings also suggest that the disposition effect is not a good noisy proxy for momentum at the lowest expected return quantile (0.05th). However, interestingly it seems to generate contrarian in returns at the highest expected returns quantile (0.95th). In the third essays, we try to discover systematic disagreements in momentum, asymmetric volatility and the idiosyncratic risk momentum return relationship between high-tech stocks and low-tech stocks. We develop several hypotheses that suggest greater momentum profits, fainter asymmetric volatility and weaker idiosyncratic risk-momentum return relation in the high-tech stocks relative to the low tech stocks. To this end, we divide 5795 stocks that are listed in the Russell 3000 index from January 1995 to December 2015 into two samples SIC code and analysed them using the Fama French with GJR-GARCH-M term. The results show that the high-tech stocks provide greater momentum profits especially for portfolios that have holding and ranking periods of less than 12 months. In most cases momentum returns in the high-tech stocks explain a symmetric response to good and bad news while the momentum returns in the low-tech stocks show an asymmetric response. Finally, the idiosyncratic risk-momentum return relation is insignificant for high-tech stocks while it is significant and negative for low-tech stocks. That is, as idiosyncratic risk increases, momentum decreases for low-tech stocks. These findings are robust to different momentum strategies and to different breakpoints.

Buried pipelines are vulnerable to the threat of corrosion. Hence, they are normally coated with a protective coating to isolate the metal substrate from the surrounding environment with the addition of CP current being applied to the pipeline surface to halt any corrosion activity that might be taking place. With time, this barrier will deteriorate which could potentially lead to corrosion of the pipe. The External Corrosion Direct Assessment (ECDA) methodology was developed with the intention of upholding the structural integrity of pipelines. Above ground indirect inspection techniques such as the DCVG which is an essential part of an ECDA, is commonly used to determine coating defect locations and measure the defect's severity. This is followed by excavation of the identified location for further examination on the extent of pipeline damage. Any coating or corrosion defect found at this stage is repaired and remediated. The location of such excavations is determined by the measurements obtained from the DCVG examination in the form of %IR and subjective inputs from experts which bases their justification on the environment and the physical characteristics of the pipeline. Whilst this seems to be a straight forward process, the factors that comes into play which gave rise to the initial %IR is not fully understood. The lack of understanding with the additional subjective inputs from the assessors has led to unnecessary excavations being conducted which has put tremendous financial strain on pipeline operators. Additionally, the threat of undiscovered defects due to the erroneous nature of the current method has the potential to severely compromise the pipeline's safe continual operation. Accurately predicting the coating defect size (TCDA) and interpretation of the indication signal (%IR) from an ECDA is important for pipeline operators to promote safety while keeping operating cost at a minimum. Furthermore, with better estimates, the uncertainty from the DCVG indication is reduced and the decisions made on the locations of excavation is better informed. However, ensuring the accuracy of these estimates does not come without challenges. These challenges include (1) the need of proper methods for large data analysis from indirect assessment and (2) uncertainty about the probability distribution of quantities. Standard mean regression models e.g. the OLS, were used but fail to take the skewness of the distributions involved into account. The aim of this thesis is thus, to come up with statistical models to better predict TCDA and to interpret the %IR from the indirect assessment of an ECDA more precisely. The pipeline data used for the analyses is based on a recent ECDA project conducted by TWI Ltd. for the Middle Eastern Oil Company (MEOC). To address the challenges highlighted above, Quantile Regression (QR) was used to comprehensively characterise the underlying distribution of the dependent variable. This can be effective for example, when determining the different effect of contributing variables towards different sizes of TCDA (different quantiles). Another useful advantage is that the technique is robust to outliers due to its reliance on absolute errors. With the traditional mean regression, the effect of contributing variables towards other quantiles of the dependent variable is ignored. Furthermore, the OLS involves the squaring of errors which makes it less robust to outliers. Other forms of QR such as the Bayesian Quantile Regression (BQR) which has the advantage of supplementing future inspection projects with prior data and the Logistic Quantile Regression (LQR) which ensures the prediction of the dependent variable is within its specified bounds was applied to the MEOC dataset. The novelty of research lies in the approaches (methods) taken by the author in producing the models highlighted above. The summary of such novelty includes: * The use of non-linear Quantile Regression (QR) with interacting variables for TCDA prediction. * The application of a regularisation procedure (LASSO) for the generalisation of the TCDA prediction model.* The usage of the Bayesian Quantile Regression (BQR) technique to estimate the %IR and TCDA. * The use of Logistic Regression as a guideline towards the probability of excavation * And finally, the use of Logistic Quantile Regression (LQR) in ensuring the predicted values are within bounds for the prediction of the %IR and POPD. Novel findings from this thesis includes: * Some degree of relationship between the DCVG technique (%IR readings) and corrosion dimension. The results of the relationship between TCDA and POPD highlights a negative trend which further supports the idea that %IR has some relation to corrosion. * Based on the findings from Chapter 4, 5 and 6 suggests that corrosion activity rate is more prominent than the growth of TCDA at its median depth. It is therefore suggested that for this set of pipelines (those belonging to MEOC) repair of coating defects should be done before the coating defect has reached its median size. To the best of the Author's knowledge, the process of employing such approaches has never been applied before towards any ECDA data. The findings from this thesis also shed some light into the stochastic nature of the evolution of corrosion pits. This was not known before and is only made possible by the usage of the approaches highlighted above. The resulting models are also of novelty since no previous model has ever been developed based on the said methods. The contribution to knowledge from this research is therefore the greater understanding of relationship between variables stated above (TCDA, %IR and POPD). With this new knowledge, one has the potential to better prioritise location of excavation and better interpret DCVG indications. With the availability of ECDA data, it is also possible to predict the magnitude of corrosion activity by using the models developed in this thesis. Furthermore, the knowledge gained here has the potential to translate into cost saving measures for pipeline operators while ensuring safety is properly addressed.

Recently, variable selection in high-dimensional data has attracted much research interest. Classical stepwise subset selection methods are widely used in practice, but when the number of predictors is large these methods are difficult to implement. In these cases, modern regularization methods have become a popular choice as they perform variable selection and parameter estimation simultaneously. However, the estimation procedure becomes more difficult and challenging when the data suffer from outliers or when the assumption of normality is violated such as in the case of heavy-tailed errors. In these cases, quantile regression is the most appropriate method to use. In this thesis we combine these two classical approaches together to produce regularized quantile regression methods. Chapter 2 shows a comparative simulation study of regularized and robust regression methods when the response variable is continuous. In chapter 3, we develop a quantile regression model with a group lasso penalty for binary response data when the predictors have a grouped structure and when the data suffer from outliers. In chapter 4, we extend this method to the case of censored response variables. Numerical examples on simulated and real data are used to evaluate the performance of the proposed methods in comparisons with other existing methods.

The goal of this thesis is to propose a new quantile regression approach to identify and estimate the quantiles of the private value conditional distribution in ascending and rst price auctions under the Independent Private Value (IPV) paradigm. The quantile regression framework provides a exible and convenient parametrization of the private value distribution, which is not a ected by the curse of dimensionality. The rst Chapter of the thesis introduces a quantile regression methodology for ascending auctions. The Chapter focuses on revenue analysis, optimal reservation price and its associated screening level. An empirical application for the USFS timber auctions suggests an optimal reservation price policy with a probability of selling the good as low as 58% for some auctions with two bidders. The second Chapter tries to address this issue by considering a risk averse seller with a CRRA utility function. A numerical exercise based on the USFS timber auctions shows that increasing the CRRA of the sellers is su cient to give more reasonable policy recommendations and a higher probability of selling the auctioned timber lot. The third Chapter develops a quantile regression methodology for rst-price auction. The estimation method combines local polynomial, quantile regression and additive sieve methods. It is shown in addition that the new quantile regression methodology is not subject to boundary issues. The choice of smoothing parameters is also discussed.

The aim of the work in this thesis is to carry out dimension reduction (DR) for high dimensional (HD) data by using statistical methods for variable selection, feature extraction and a combination of the two. In Chapter 2, the DR is carried out through robust feature extraction. Robust canonical correlation (RCCA) methods have been proposed. In the correlation matrix of canonical correlation analysis (CCA), we suggest that the Pearson correlation should be substituted by robust correlation measures in order to obtain robust correlation matrices. These matrices have been employed for producing RCCA. Moreover, the classical covariance matrix has been substituted by robust estimators for multivariate location and dispersion in order to get RCCA. In Chapter 3 and 4, the DR is carried out by combining the ideas of variable selection using regularisation methods with feature extraction, through the minimum average variance estimator (MAVE) and single index quantile regression (SIQ) methods, respectively. In particular, we extend the sparse MAVE (SMAVE) reported in (Wang and Yin, 2008) by combining the MAVE loss function with different regularisation penalties in Chapter 3. An extension of the SIQ of Wu et al. (2010) by considering different regularisation penalties is proposed in Chapter 4. In Chapter 5, the DR is done through variable selection under Bayesian framework. A flexible Bayesian framework for regularisation in quantile regression (QR) model has been proposed. This work is different from Bayesian Lasso quantile regression (BLQR), employing the asymmetric Laplace error distribution (ALD). The error distribution is assumed to be an infinite mixture of Gaussian (IMG) densities.

The focus of this thesis is on index tracking that aims to replicate the movements of an index of a specific financial market. It is a form of passive portfolio (fund) management that attempts to mirror the performance of a specific index and generate returns that are equal to those of the index, but without purchasing all of the stocks that make up the index. Additionally, we consider the problem of out-performing the index - Enhanced Indexation. It attempts to generate modest excess returns compared to the index. Enhanced indexation is related to index tracking in that it is a relative return strategy. One seeks a portfolio that will achieve more than the return given by the index (excess return). In the first approach, we propose two models for the objective function associated with choice of a tracking portfolio, namely; minimise the maximum absolute difference between the tracking portfolio return and index return and minimise the average of the absolute differences between tracking portfolio return and index return. We illustrate and investigate the performance of our models from two perspectives; namely, under the exclusion and inclusion of fixed and variable costs associated with buying or selling each stock. The second approach studied is that of using Quantile regression for both index tracking and enhanced indexation. We present a mixed-integer linear programming of these problems based on quantile regression. The third approach considered is on quantifying the level of uncertainty associated with the portfolio selected. The quantification of uncertainty is of importance as this provides investors with an indication of the degree of risk that can be expected as a result of holding the selected portfolio over the holding period. Here a bootstrap approach is employed to quantify the uncertainty of the portfolio selected from our quantile regression model.

This thesis focuses on applying order-statistics-based inferences on lifetime analysis and financial risk measurement. The first problem is raised from fitting the Weibull distribution to progressively censored and accelerated life-test data. A new orderstatistics- based inference is proposed for both parameter and con dence interval estimation. The second problem can be summarised as adopting the inference used in the first problem for fitting the generalised Pareto distribution, especially when sample size is small. With some modifications, the proposed inference is compared with classical methods and several relatively new methods emerged from recent literature. The third problem studies a distribution free approach for forecasting financial volatility, which is essentially the standard deviation of financial returns. Classical models of this approach use the interval between two symmetric extreme quantiles of the return distribution as a proxy of volatility. Two new models are proposed, which use intervals of expected shortfalls and expectiles, instead of interval of quantiles. Different models are compared with empirical stock indices data. Finally, attentions are drawn towards the heteroskedasticity quantile regression. The proposed joint modelling approach, which makes use of the parametric link between the quantile regression and the asymmetric Laplace distribution, can provide estimations of the regression quantile and of the log linear heteroskedastic scale simultaneously. Furthermore, the use of the expectation of the check function as a measure of quantile deviation is discussed.

The growth of the financial risk management industry has been motivated by the increased volatility of financial markets combined with the rapid innovation of derivatives. Since the 1970s, several financial crises have occurred globally with devastating consequences for financial and non-financial institutions and for the real economy. The most recent US subprime crisis led to enormous losses for financial and non-financial institutions and to a recession in many countries including the US and UK. A common lesson from these crises is that advanced financial risk management systems are required. Financial risk management is a continuous process of identifying, modeling, forecasting and monitoring risk exposures arising from financial investments. The Value at Risk (VaR) methodology has served as one of the most important tools used in this process. This quantitative tool, which was first invented by JPMorgan in its Risk-Metrics system in 1995, has undergone a considerable revolution and development during the last 15 years. It has now become one of the most prominent tools employed by financial institutions, regulators, asset managers and nonfinancial corporations for risk measurement. My PhD research undertakes a comprehensive and practical study of market risk modeling in modern finance using the VaR methodology. Two newly developed risk models are proposed in this research, which are derived by integrating volatility modeling and the quantile regression technique. Compared to the existing risk models, these two new models place more emphasis on dynamic risk adjustment. The empirical results on both real and simulated data shows that under certain circumstances, the risk prediction generated from these models is more accurate and efficient in capturing time varying risk evolution than traditional risk measures. Academically, the aim of this research is to make some improvements and extensions of the existing market risk modeling techniques. In practice, the purpose of this research is to support risk managers developing a dynamic market risk measurement system, which will function well for different market states and asset categories. The system can be used by financial institutions and non-financial institutions for either passive risk measurement or active risk control.

The motivation for this thesis came from the provision of a large data set from Saudi Arabia giving anthropometric measurements of children and adolescents from birth to eighteen years of age, with a requirement to construct growth charts. The construction of these growth charts revealed a number of issues particularly in the respect to statistical inference relating to quantile regression. To investigate a range of different statistical inference procedures in parametric quantile regression in particular the estimation of the confidence limits of the ?th (?? [0, 1]) quantile, a number of sets of simulated data in which various error structures are imposed including homoscedastic and heteroscedastic structures were developed. Methods from the statistical literature were then compared with a method proposed within this thesis based on the idea of Silverman's (1986) kernel smoothing. This proposed bootstrapping method requires the estimation of the conditional variance function of the fitted quantile. The performance of a variety of variance estimation methods combined within the proposed bootstrapping procedure are assessed under various data structures in order to examine the performance of the proposed bootstrapping approach. The validity of the proposed bootstrapping method is then illustrated using the Saudi Arabian anthropometric data.

This thesis investigates the determinants of the use of debt and leasing in the UK using a comprehensive measure of debt and leases, in recognition of the link between lease and debt-type financing decisions, based on financial contracting theory and the tax advantage hypothesis. The design of the study takes account three lacunae in our current understanding of this topic. Firstly, despite the fact that the capital structure literature is voluminous, it is perhaps surprising that relatively little research has been carried out on lease finance, given its significant role as a major source of finance for many firms. Secondly, the role of tax in the capital structure decision is unclear. Empirically testing for tax effects is challenging because spurious relationships may exist between the financing decision and many commonly used tax proxies. More importantly, our understanding of the impact of taxes on UK financing decisions is far from complete, especially since several major corporate tax reforms have taken place in the last decade. Thirdly, empirical evidence on capital structure determinants is also voluminous but far from conclusive. Notably, contradictory signs and significance levels are commonly observed. Using the standard regression approach invariably involves identification of the average behaviour of firms, and therefore does not measure diversity across firms. In response to these three major issues, this study employs empirical research methods, namely cross-sectional pooled regression, static and dynamic panel data regression, and quantile regression to analyse a large sample of 361 non-financial firms, drawn from the FTSE 350 and FTSE All-Small indices over the tax years 1995 through 2003. The operating lease data are estimated using the constructive capitalisation method while the simulated before-financing marginal tax rate is used to proxy for the firms’ tax status. The endogeneity of corporate tax status is evident since the use of simple tax proxy, the effective tax rate, leads to a spurious negative relation between debt usage and tax rates. The problem was avoided with a better measure of tax variable that is the simulated before-financing marginal tax rate where it is found that the empirical relationships between the tax factor and debt and leasing are consistent with those theoretical predictions. Furthermore, there is a clear distinction between the effect of taxes on debt and leasing where the firm’s marginal tax status is only relevant when managers make decisions on debt financing. The use of quantile regression method in the present study represents a novel approach in investigating the determinants of the use of debt and leasing. The results reveal that the determinants of debt and leasing are heterogeneous across the whole distribution of firms, consistent with the notion of heterogeneity as promoted by Beattie et al. (2006), but contradicting their claim that the large-scale regression approach cannot measure firms’ diversity. This finding implies that average model results (e.g., from OLS or panel data models) may not apply to the tails of debt and leasing levels, and hence assuming that the determinants of debt and leasing decisions are the same for all firms in the economy is clearly unrealistic. Using the dynamic panel data model, this thesis confirms that debt and leasing are substitutes rather than complements, and that the degree of substitutability is more pronounced among smaller firms, where the degree of information asymmetry is greater. More importantly, the use of a joint specification for debt and leasing improves our understanding of the determinants of the two fixed-claim financing instruments. There is also significant evidence to support the view that firm characteristics affect contracting costs which in turn impact on the choice between alternative forms of finance, namely equity, debt and leasing.

In the first part of this work, we propose a novel efficient sampling method for measurement-constrained data. Under “measurement constraints,” responses are expensive to measure and initially unavailable on most of records in the dataset, but the covariates are available for the entire dataset. Our goal is to sample a relatively small portion of the dataset where the expensive responses will be measured and the resultant sampling estimator is statistically efficient. Measurement constraints require the sampling probabilities can only depend on a very small set of the responses. A sampling procedure that uses responses at most only on a small pilot sample will be called “response-free.” We propose a response-free sampling procedure (OSUMC) for generalized linear models (GLMs). Using the A-optimality criterion, i.e., the trace of the asymptotic variance, the resultant estimator is statistically efficient within a class of sampling estimators. We establish the unconditional asymptotic distribution of a general class of response-free sampling estimators. This result is novel compared with the existing conditional results obtained by conditioning on both covariates and responses. Under our unconditional framework, the subsamples are no longer independent and new martingale techniques are developed for our asymptotic theory. We further derive the A-optimal response-free sampling distribution. Since this distribution depends on population level quantities, we propose the Optimal Sampling Under Measurement Constraints (OSUMC) algorithm to approximate the theoretical optimal sampling. Finally, we conduct an intensive empirical study to demonstrate the advantages of OSUMC algorithm over existing methods in both statistical and computational perspectives. We find that OSUMC’s performance is comparable to that of sampling algorithms that use complete responses. This shows that, provided an efficient algorithm such as OSUMC is used, there is little or no loss in accuracy due to the unavailability of responses because of measurement constraints. In the second part of this work, we develop uniform inference methods for the conditional mode based on quantile regression. Specifically, we propose to estimate the conditional mode by minimizing the derivative of the estimated conditional quantile function defined by smoothing the linear quantile regression estimator, and develop two bootstrap methods, a novel pivotal bootstrap and the nonparametric bootstrap, for our conditional mode estimator. Building on high-dimensional Gaussian approximation techniques, we establish the validity of simultaneous confidence rectangles constructed from the two bootstrap methods for the conditional mode. We also extend the preceding analysis to the case where the dimension of the covariate vector is increasing with the sample size. Finally, we conduct simulation experiments and a real data analysis using U.S. wage data to demonstrate the finite sample performance of our inference method. The supplemental materials include the wage dataset, R codes and an appendix containing proofs of the main results, additional simulation results, discussion of model misspecification and quantile crossing, and additional details of the numerical implementation. In the third part of this work, we develop a multi-round aggregated one-step estimator and a scalable bootstrap method for distributed sparse least absolute deviation (LAD) regression with high-dimensional covariates. The proposed one-step estimator is based on multi-round distributed quantile regression andlinear regression estimators. We derive convergence rates and sparsity proper- ties of the new multi-round estimators and show that our multi-round one-step estimator requires less restrictive sample complexity than the one-shot aggregation for valid inference. We also develop a novel pivotal bootstrap for simultaneous inference that is scalable to the distributed setting. Building on high-dimensional Gaussian approximation techniques, we establish the validity of simultaneous confidence rectangles constructed from the pivotal boot- strap. Finally, we conduct numerical experiments using the simulated data, which demonstrate encouraging performance of our methods.

Investments of public dollars on highway and transit infrastructure are influenced by the anticipated demands for highways and public transportations or traffic and transit ridership forecasts. The purpose of this study is to understand the accuracy of road traffic forecasts and transit ridership forecasts, to identify the factors that affect their accuracy, and to develop a method to estimate the uncertainty inherent in those forecasts. In addition, this research investigates the pre-pandemic decline in transit ridership across the US metro areas since 2012 and its influence on the accuracy of transit forecasts. The sample of 1,291 road projects from the United States and Europe compiled for this research shows that measured traffic is on average 6% lower than forecast volumes, with a mean absolute deviation of 17% from the forecast. Higher volume roads, higher functional classes, shorter time spans, and the use of travel models all improved accuracy. Unemployment rates also affected accuracy—traffic would be 1% greater than forecast on average, rather than 6% lower, if we adjust for higher unemployment during the post-recession years (2008 to 2014). Forecast accuracy was not consistent over time: more recent forecasts were more accurate, and the mean deviation changed direction. Similarly for 164 large-scale transit projects, the observed ridership was about 24.6% lower than forecasts on average. The accuracy depends on the mode, length of the project, year the forecast was produced as well as socio-economic and demographic changes from the production to observation year. In addition, we have found evidence of recent changes in transit demand to be affecting the transit ridership forecast accuracy. From 2012 to 2018, bus ridership decreased by almost 15% and rail ridership decreased by about 4% on average across the metropolitan areas in the United States. This decline is unexpected, because it coincided with the period of economic and demographic growth: indicators typically associated with rising transit ridership. We found that the advent of new mobility options in ride hailing services, bike and scooter shares as well as declining gas prices and increasing transit fares have the highest impact on ridership decline. Adjusting the ridership forecasts for these factors in a hypothetical scenario saw an improved transit ridership forecast performance. Despite the advances in modeling techniques and the availability of rich travel data over the years, expecting perfect forecasts (where observations are equal to the forecasts), may not be prudent because of its forward-facing nature. Forecasts need to convey their inherent uncertainty so that planners and policymakers can take that into account when they are making any decision about a project. The existing methods to quantify the uncertainty rely on flawed assumptions regarding input variability and interaction and are significantly resource intensive. An alternate method is one that considers the uncertainty inherent in the travel demand models themselves based on empirical evidence. In this research, I have developed a tool to quantify the uncertainty in traffic and transit ridership forecasts through a retrospective evaluation of the forecast accuracy from the two largest available databases of traffic and transit ridership forecasts. The factors associated with the accuracy and the recent decline in transit ridership lead the formulation of quantile regression as a new method to quantify the uncertainty in forecasts. Together with a consideration of decision intervals or breakpoints where a project decision might change, such ranges can be used to quantify project risk and produce better forecasts.

Wind generation in Texas has been growing rapidly, and it is poised to create major disruptive shifts in the generation only market of the Electricity Reliability Council of Texas. The average real time price of electricity has been declining in this market in part due to the merit-order effect, where low marginal cost variable renewable generation undercuts thermal baseload generators with higher operating costs. In a generation only market, depressed energy prices can reduce the economic viability of baseload generators, threatening grid reliability with narrow reserve capacity margins. This work performs empirical analysis on a large market dataset using quantile regression to quantify how the seasonal, diurnal, and regional variation of merit-order effect varies in intensity throughout the distributions of price and as wind generation has increased over time. We demonstrate that while the merit-order effect has increased in intensity alongside increased wind penetration for high percentiles of market prices, the effect is overall reducing in magnitude relative to the amount of wind generation in the system, from a price reduction on top quantiles of price of $11 per GWh of wind generated in 2011 to a respective $5 decrease in prices for the same quantity of wind generation in 2019. This finding alleviates some concerns of baseload generator profitability in the long-term as the price depression from the merit-order effect trends towards zero. We follow with a discussion of the implications for the market as large amounts of solar are poised to come online in the coming years, which will accordingly exert a large but temporary merit-order effect as penetration begins to reach significant amounts. We conclude with policy recommendations to mitigate any potential adverse consequences on grid reliability due to the upcoming short-term price disruptions that will be associated with the ramp up of solar PV capacity in the grid

This dissertation develops quantitative models to support medical decision making of statininitiation considering the uncertainty in disease progression for prediabetes patients. A mathematical model is built to help medical decision-makers take action of statin initiation under uncertainty in future prediabetes progressions. The association between cholesterol drug use, such as statin, and elevating glucose level attracted considerable amounts of attention in the literature. Statin effects on glucose vary with respect to different levels of glucose. The first chapter of this dissertation introduces the problem and an overview of the tools that will be used to solve it. In the second chapter of this dissertation, we use quantile regression to investigate the statin effects on different glucose quantiles. The third chapter is devoted to address the problem of estimating transition probabilities for the prediabetes populations for different levels of lipid ratios (i.e., ratios of total cholesterol to high-density lipoprotein) from cross-sectional data. We also show the risk of prediabetes as a function of age using a Bayesian approach. These parameters are used in the implementation of the Markov Decision Process (MDP) to estimate the best point in time, i.e., age to start statin treatment, which is discussed in the fourth chapter of the dissertation. Parameter estimation plays a crucial role in our model. Therefore, our fifth problem to tackle is to provide the optimal policy for statin initiation by considering stochastic progression under uncertainty for lipid ratio transition probabilities. A robust MDP problem is formulated and an optimal policy for statin initiation is provided. Structural properties of the robust MDP problem are proved. Additionally, sufficient conditions for the existent of robust MDP are introduced.

High-performance computing (HPC) variability management is an important topic in computer science. Research topics include experimental designs for efficient data collection, surrogate models for predicting the performance variability, and system configuration optimization. Due to the complex architecture of HPC systems, a comprehensive study of HPC variability needs large-scale datasets, and experimental design techniques are useful for improved data collection. Surrogate models are essential to understand the variability as a function of system parameters, which can be obtained by mathematical and statistical models. After predicting the variability, optimization tools are needed for future system designs. This dissertation focuses on HPC input/output (I/O) variability through three main chapters. After the general introduction in Chapter 1, Chapter 2 focuses on the prediction models for the scalar description of I/O variability. A comprehensive comparison study is conducted, and major surrogate models for computer experiments are investigated. In addition, a tool is developed for system configuration optimization based on the chosen surrogate model. Chapter 3 conducts a detailed study for the multimodal phenomena in I/O throughput distribution and proposes an uncertainty estimation method for the optimal number of runs for future experiments. Mixture models are used to identify the number of modes for throughput distributions at different configurations. This chapter also addresses the uncertainty in parameter estimation and derives a formula for sample size calculation. The developed method is then applied to HPC variability data. Chapter 4 focuses on the prediction of functional outcomes with both qualitative and quantitative factors. Instead of a scalar description of I/O variability, the distribution of I/O throughput provides a comprehensive description of I/O variability. We develop a modified Gaussian process for functional prediction and apply the developed method to the large-scale HPC I/O variability data. Chapter 5 contains some general conclusions and areas for future work.

The thesis is divided in three sections of interconnected topics. Motivated by applications from precision medicine, we consider the problem of estimating an optimal treatment regime (or individual optimal decision rule) based on right-censored survival data. We consider a non-parametric approach that maximizes the expected mean restricted survival time of the potential outcome distribution. Comparing with existing methods, our approach does not need to assume the decision rule belongs to a restricted class (e.g., class of index rules) and can accommodate high-dimensional covariates. We investigate the theory of the estimated optimal treatment regime. Monte Carlo studies and a real data example are used to demonstrate the performance of our proposed method. Random forests are widely used today for various purposes such as regression classification, survival analysis however its theoretical properties are not yet explored completely. We propose a quantile random forest estimator which considers sub-sampling instead of complete bootstrap samples as in Meinshausen[2006]. We study the point wise asymptotics of quantile random forest estimator proposed by rendering it in the framework of U-statistics. We prove point-wise weak convergence to normality and also propose a consistent estimator of the variance. We further explore the asymptotic behavior of the proposed estimator via a simulation study. Measuring the efficacy of a treatment or policy can involve data heterogeneity. In such cases, the entire conditional distributional impact of the treatment is important rather than just a discrete metric such as the average treatment effect. Quantiles inform more about the distribution than an average and multiple quantiles can be used together to get an idea about the entire distribution. In the context of survival analysis with censored data, we propose a quantile regression model estimated using survival random forest. We further extend this to estimate quantile treatment effects under censoring. We show the efficacy of the proposed method via simulations. We also demonstrate using this method and interpreting quantile effect by analysing a colon cancer dataset.

With advances in high-throughput techniques, the availability of large-scale omics data has revolutionized the fields of medicine and biology, and has offered a better understanding of the underlying biological mechanisms. However, the high-dimensionality and the unknown association structure between different data types make statistical integration analyses challenging. In this dissertation, we develop three dimensionality reduction methods to detect nonlinear association structure using omics data. First, we propose a method for variable selection in a nonparametric additive quantile regression framework. We enforce a network regularization to incorporate information encoded by known networks. To account for nonlinear associations, we approximate the additive functional effect of each predictor with the expansion of a B-spline basis. We implement the group Lasso penalty to achieve sparsity. We define the network-constrained penalty by regulating the difference between the effect functions of any two linked genes (predictors) in the network. Simulation studies show that our proposed method performs well in identifying truly associated genes with fewer falsely associated genes than alternative approaches. Second, we develop a canonical correlation analysis (CCA)-based method, canonical distance correlation analysis (CDCA), and leverage the distance correlation to capture the overall association between two sets of variables. The CDCA allows untangling linear and nonlinear dependence structures. Third, we develop the sparse CDCA (sCDCA) method to achieve sparsity and improve result interpretability by adding penalties on the loadings from the CDCA. The sCDCA method can be applied to data with large dimensionality and small sample size. We develop iterative majorization-minimization-based coordinate descent algorithms to compute the loadings in the CDCA and sCDCA methods. Simulation studies show that the proposed CDCA and sCDCA approaches have better performance than classical CCA and sparse CCA (sCCA) in nonlinear settings and have similar performance in linear association settings. We apply the proposed methods to the Framingham Heart Study (FHS) to identify body mass index associated genes, the association structure between metabolic disorders and metabolite profiles, and a subset of metabolites and their associated type 2 diabetes (T2D)-related genes.

Despite its popularity in diverse disciplines, quantile regression methods are primarily designed for the continuous response setting and cannot be directly applied to the discrete (or count) response setting. There can also be challenges when modeling count responses, such as the presence of excess zero counts, formally known as zero-inflation. To address the aforementioned challenges, we propose a comprehensive model-aware strategy that synthesizes quantile regression methods with estimation of zero-inflated count regression models. Various competing computational routines are examined, while residual analysis and model selection procedures are included to validate our method. The performance of these methods is characterized through extensive Monte Carlo simulations. An application to the Oregon Health Insurance Experiment will also be discussed. We then extend our methods to the setting of longitudinal data with zero-inflated count responses, where the goal is to study identification and estimation of conditional quantile functions for such data. We first show that conditional quantile functions for discrete responses are identified in zero-inflated models with subject heterogeneity. Then, we develop a simple three-step approach to estimate the effects of covariates on the quantiles of the response variable. We present a simulation study to show the small sample performance of the estimator. Finally, we illustrate our model using the RAND Health Insurance Experiment data and the Combined Pharmacotherapies and Behavioral Interventions (COMBINE) data.

This dissertation examines topics related to renewable energy development and investment planning, energy markets, environment degradation and economic development. The substantial ecological costs of deforestation are well known and considered globally important due to biodiversity loss, land degradation, soil erosion, and contributions to climate change. The first essay focuses upon understanding the tradeoff between development and deforestation in Africa. In the second essay, spatial analysis and Geographic Information System (GIS) are applied to determine potential locations for wind farms development in the state of West Virginia. Lastly, the third essay examines the role of wind power penetration on wholesale electricity market. The first essay explores the relationship between economic growth and deforestation in African countries. During the past half-century, the continent of Africa has suffered massive losses of forested areas due to the changing structure of economies, increasing population, and expanding globalization. This research examines statistical evidence for the Environmental Kuznets Curve (EKC) hypothesis as applied to deforestation occurring within Africa from 1990 to 2016. Changes in forest cover data are explained with Generalized Method of Moments (GMM) estimators to overcome the endogeneity problems arising from reverse causality between deforestation and explanatory variables. The empirical results of a panel GMM confirm the EKC hypothesis is valid for deforestation in Africa with a turning point estimated to be US $3,000. Heterogenous panel non-causality findings suggest that Africa could deter and reverse deforestation through appropriate land-use and forest products trade policies, and the consequences of these policies would not impact their economic growth. In the second essay, a multi-criteria decision analysis employing Analytic Hierarchy Process (AHP) and GIS are used for assessment of potential sites for future utility-scale wind farms in West Virginia. Worldwide, demand is increasing for renewable energy. While wind power is a proven, sustainable energy source, siting can be challenging. Identifying potential sites for wind turbines is a significant step in renewable energy resource planning. Wind turbine site suitability is primarily dependent upon wind speed at a location along with other environmental, social, and economic factors. It is critical to arrive at a robust wind farm decision to improve public acceptance, preserve the environment, and maintain pristine habitats. This research builds upon previous studies and contributes to the literature by incorporating two important components into siting: (1) inclusion of critical wildlife habitat for birds and bats as an elimination criterion within the AHP, and (2) the participation by wind power experts in the AHP decision-making process. By incorporating expert opinions with the weighing of ten siting factors, about 70,000 hectares of land are identified as 'highly suitable' for wind power development throughout the state of West Virginia. This area represents the potential to yield an estimated 29,000 MW of future utility-scale wind power capacity, which is larger than the current coal dominated electricity generation capacity in West Virginia. The third essay examines the wind power penetration impacts on wholesale electricity markets. Using data from two wholesale electricity markets (Pennsylvania – New Jersey – Maryland (PJM) and Electric Reliability Council of Texas (ERCOT)), four energy policy questions are addressed: (1) How much does wind power integration impact wholesale electricity prices under different markets? (2) Does the merit-order effect (MOE) exist at different quantiles of wholesale electricity prices? (3) What drives the day-ahead market (DAM) and real-time market (RTM) prices at different market conditions in both markets? (4) Does the increasing penetration of wind power undermine its market value along with the market values of other generating technologies? To answer these questions, quantile regression is used to obtain coefficient estimates that indicate wind penetration has unequal impacts on wholesale electricity prices and market values across quantiles, reinforcing the need for this type of analysis. The empirical analyses confirmed the existence of the merit-order effect across different quantiles of the conditional distribution of wholesale prices for both DAM and RTM, implying that the increasing deployment of wind power for electricity generation significantly suppresses the wholesale electricity prices in the PJM market. Contrary to the PJM estimations, merit-order effects are confirmed across quantiles of wholesale prices for only the DAM in the ERCOT market. Furthermore, the findings show that as wind generation expands within the market, the revenue earned by wind power producers reduces across all quantiles of the conditional distribution of its unit revenue. Specifically, each additional GWh increase in electricity from wind is associated with a fall in its unit revenues across quantiles by an amount that ranges from approximately $0.01/MWh to $0.06/MWh. Results also confirm cross-cannibalization impacts such that each additional GWh increase from wind is associated with decreased gas and baseload unit revenues across all quantiles ranging from $0.02/MWh to $0.06/MWh. Contrary to unit revenue results, there is weak evidence of increasing wind supply's cannibalization effect for value factor as positive impacts occur below the 90% quantile and negative impacts occur at quantiles 90% and greater. The negative impacts of wind power on gas and baseload generators demonstrate the need for corrective policies.

Linear quantile mixed modeling is a diverse statistical tool that can replace traditional least squares modeling for analyzing data whose sampling method has some form of clustering and whose response has trends that differ for each quantile level. In this article, we will evaluate the effectiveness of this modeling method through the use of the lqmm package in R[2]. Simulations and n applied data analysis will be performed to evaluate the performance of the lqmm() function on different types of datasets. We will also introduce background on quantile based mixed modeling and give descriptions of the output and main commands of the lqmm() function.

Sequential change point analysis aims to detect structural change as quickly as possible when the process state changes. A good sequential change point detection procedure is expected to minimize the detection delay time and the risk of raising false alarm. Existing sequential change point detection methods cannot be applicable for high-dimensional data because they are univariate in nature and thus present challenges.In the first part of the dissertation, we develop a monitoring method to detect structural change in smoothly clipped absolute deviation (SCAD) penalized regression model for high-dimensional data after the historical sample with the sample size m. The unknown pre-change regression coefficients are replaced by the SCAD penalized estimator. The asymptotic properties of the proposed test statistics are derived. We conduct a simulation study to evaluate the performance of the propose method. The proposed method is applied to the gene expression in the mammalian eye data to detect changes sequentially.In the second part of the dissertation, we develop a sequential change point detection method to monitor structural changes in SACD penalized quantile regression (SPQR) model for high-dimensional data. We derive the asymptotic distributions of the test statistic under the null and alternative hypotheses. Furthermore, to improve the performance of the SPQR method, we propose the Post-SCAD penalized quantile regression estimator (P-SPQR) for high-dimensional data. Simulations are conducted under different scenarios to study the finite sample properties of the SPQR and P-SPQR methods. A real data application is provided to demonstrate the effectiveness of the method.In the third and fourth part of the dissertation, we investigate the change point problem for Skew-Normal distribution and three parameter Weibull distribution respectively. Besides detecting and obtaining the point estimate of a change location, we propose an estimation procedure based on the confidence distribution (CD) along with the modified information criterion (MIC) to construct the confidence set for the change location. Simulations are conducted to evaluate the performance of the proposed method in terms of powers, coverage probabilities and average lengths of confidence sets. Real data applications are provided in each part to illustrate the performance of the proposed methods.

Complex systems consist of many interacting components. Understanding the connections between these components is critical for evaluating the system's stability and for predicting its future state. Such systems can be represented by a network, with nodes denoting the individual participants and edges indicating associations between members. In this dissertation, we explore methods of learning financial and biological networks. We begin by estimating networks of large financial institutions, applying pairwise and system-wide Granger causality methods to time series of the firms' monthly stock returns. We consider both mean-based Granger causality as well as a tail-based version that relies on quantile regression, from which we can distinguish interfirm connections that exist during different market conditions. Next, we build upon these ideas by constructing financial networks from high-frequency (intraday) trade data using machine learning techniques. In both the low- and high-frequency settings, we demonstrate how the networks can be used to detect critical economic events, ex post, and to identify important financial institutions. Finally, we use partial correlation and debiased graphical Lasso to estimate a network of genes based on their essentiality profiles. This network can be used to identify groups of interacting genes that may be promising candidates for further experimental validation.

The key focus of this dissertation is on how to understand and measure treatment effect heterogeneity in experimental or quasi-experimental evaluations of educational policy interventions. When testing the impact of an intervention, it can be important to know not just the overall or average effect of the intervention on key outcomes but also how the effect varies across subgroups of study participants, as defined by several dimensions including their pre-treatment characteristics, site-level contexts, and the distribution of an outcome measure. Heterogeneity or variation in effects has critical implications for understanding how interventions work and which aspects of an intervention's implementation are most closely associated with its effectiveness. This dissertation examines both methodological and substantive questions that pertain to such heterogeneity.In Chapter 1, I examine Bayesian hierarchical models for multi-site trials that allow estimation of site-specific treatment effects and their distribution. Modeling site-specific effects using observed data is a critical component in understanding the results of multisite trials. A standard approach leveraging Bayesian methods is to rely on Gaussian distributional assumptions and to use the posterior means (PM) of the random effects. The standard approach can be misleading, however, in the estimation of individual site-specific effects and their empirical distribution and ranks. In this chapter, I review the following two strategies developed to improve inferences regarding site-specific effects: (a) relaxing the normality assumption by flexible modeling of the random-effects distribution using Dirichlet process mixture (DPM) models, and (b) replacing the choice of PM as the summary of the posterior by alternative estimators, such as the constrained Bayes (CB) or the triple-goal (GR) estimators. I then examine when and to what extent the two strategies and combinations thereof work or fail under varying conditions. In Chapter 2, I study methodological issues arise in the practice where Bayesian quantile regression (BQR) models are applied. The BQR models allow us to study treatment effect heterogeneity across the distribution of an outcome measure such as a student achievement test score. In BQR, the most commonly applied likelihood is the asymmetric Laplace (AL) likelihood because it is computationally convenient for Markov chain Monte Carlo algorithms. For easier computation, the scale parameter of the AL distribution is often fixed at a pre-estimated value or an arbitrary constant. This paper demonstrates that posterior inference in BQR with an AL likelihood is highly sensitive to the choice of the fixed scale parameter. Based on sensitivity analyses using Monte Carlo simulations and a real data example, I make two claims. First, not only the variance directly obtained from the posterior distribution, but also the adjusted posterior variance proposed by Yang et al. (2015), is highly sensitive to the value of the scale parameter. Second, in finite samples, both conventional and Bayesian point estimators can be biased at extreme quantiles. Researchers need to be aware of the possibility of low coverage probabilities at extreme quantiles mainly caused by biased point estimates. In Chapter 3, I examine the use of the grouped/multilevel instrumental variable (IV) quantile regression approach, a quantile extension of Hausman and Taylor (1981). The common approach of estimating the shift of group-level (level-2) averages of individual-level (level-1) outcomes may mask important but more subtle effects on the outcome distribution. For example, a school-level intervention may have little effect on school-level average test score but may cause a substantial shift in the lower quantiles of the within-school test score distributions if the intervention is particularly beneficial for low-performing students. As one real-world empirical example, I used the grouped/multilevel IV quantile approach to estimate the effects of district-level increases in per-pupil spending on quantiles of the within-district distribution of school quality measures. I show how new dollars flowing to districts did affect varying mixes of teachers and organizational practices inside schools, but in ways that mitigated against narrowing disparities. Better funded high schools reduced access to college-prep courses relative to electives, and novice teachers were often assigned to courses serving English learners, inequities that widened in high-poverty schools.

Quantile regression is a useful tool for testing the possible effect of covariates, especially when the effect is heterogeneous. Classical methods designed to test the effect at one quantile level can be sensitive to the quantile level choice. In this dissertation, we propose a regional quantile regression rank test as a generalization of the rank test at an individual quantile level. The proposed test statistic allows us to detect the treatment effect for a prespecified quantile interval by integrating the regression rank scores over the quantile region of interest. A new model-based bootstrap method is constructed to estimate the null distribution of the test statistic. A simulation study is conducted to demonstrate the validity and usefulness of the proposed test. We also illustrate the power of the proposed test using sub-samples from the 2016 US birth weight data. We then generalize the regional quantile regression rank test to censored quantile regression settings. We propose a censored version of the regression rank score using the redistribution of the probability mass for each censored observation. The model-based bootstrap algorithm is also generalized to implement the test. We illustrate the advantage of the proposed method through simulation and apply our method to study how the early environment condition influences the survival time of the bighorn sheep. In a related study, we consider the genome-wide association study where the goal is to select genes that are associated with an outcome of interest. One major challenge for the genome-wide association study is how to handle the possible interactions between the genes and the environment. We propose a two-stage model, including one that relies on the conditional quantile levels of the outcome variables, to allow the genes to have comprehensive interactions with the environment. We use the two-stage model to study a lung cancer data set to identify new genes that can potentially influence lung cancer patients' survival time.

This dissertation consists of three papers on the economics of natural resources. Two of these examine the impact of price on consumption, and the third illustrates the benefits to applying big data methods to the estimation of fishery production functions.Chapter 1 estimates the price elasticity of demand for residential water across the distribution of users and over the course of time after the change. Using monthly billing data provided by a private utility in Phoenix, Arizona, the distribution of price responses is estimated via quantile regression. The results indicate that most households reduced their usage about 200 gallons per month, while the top 20% reduced usage by 500 to 800 gallons per month. Converting this into a percentage change to compute the elasticity inverts the results such that the lowest 20% of households have the largest percentage reduction in use. The reductions in usage take four months to emerge, after which it is apparent that summer reductions are greater than winter reductions.Chapter 2 explores the strategic behaviors exhibited by households in response to high-low pricing patterns for purchases of canned tuna, and how these behaviors differ for purchases of eco-labeled brands. Promotional price elasticities are estimated using a demand system for six retailers over five years. The promotional price elasticity for the eco-labeled brand (-2.8) is similar to Bumble Bee (-2.2) and StarKist (-2.9), implying that purchases of eco-labeled canned tuna respond similarly to sales prices. A survival model is estimated using household scanner panel data to analyze the inter-purchase timing decision, with the results showing that stockpiling behaviors are similar between eco-labeled and conventional tuna but price is a more significant factor in accelerating purchases for the eco-labeled brand.Chapter 3 illustrates the efficacy of LASSO variable and instrument selection methods for estimating production in fisheries. Production functions are estimated using traditional model selection and LASSO model selection for both ordinary least squares and instrumental variables methods. The results show that LASSO performs marginally better at ordinary least squares and significantly better for instrumental variables, which tests for endogeneity indicate should be the preferred method.

Abstract: With accelerating technological advancements, functional data analysis is of ever-growing importance in statistics, engineering, and medicine as the collection, storage, and analysis of data becomes ingrained in every aspect of modern life beyond any one field of study. From continuous biometric measurements to environmental monitoring to medical imaging, data collected across time, space, and mathematical manifolds in general are increasingly common. The advent of ``big data'' ensures that the rate, volume, and complexity of collected data will only continue to grow. Despite its richness, the high dimensionality of functional data is inherently challenging to incorporate into statistical models in both theory and practice. This thesis is primarily concerned with incorporating multiple scalar-valued functional covariates, each with a high-dimensional domain but observed in a discrete, uniform grid, into functional quantile regression models for a scalar response. This type of functional data is ubiquitous in science and medicine as imaging data observed across spatiotemporal dimensions in a tensor format. The existing accommodation of functional and tensor-valued covariates in generalized linear models does not extend immediately to the quantile setting, although such a development would be useful in practice. Indeed, quantile models are well-known to be more efficient and robust for non-Gaussian, heavy-tailed error distributions or when outliers are present---typically the case with real-world data. Throughout this work, we emphasize direct regularization of tensor effects for more generalizable models and interpretable signal recovery for imaging data. The Tucker tensor decomposition is the main tool used in this thesis: we assume a low-dimensional representation of a tensor with a particular polyadic structure to reduce the dimension of the parameter space and make model estimation feasible. We obtain this decomposition in a supervised manner, relying on partial quantile covariance between tensor covariates and the scalar response, similar to partial least squares in traditional linear regression. We estimate decomposition parameters and fit the proposed $q$-dimensional tensor quantile regression (\qdt{}) model by minimizing quantile loss. To address the non-convexity and non-differentiability of the loss in Tucker tensor decomposition parameters, we use a block relaxation technique and a continuously differentiable smoothing approximation of the quantile loss. After proposing a new algorithm and gradient-based implementation for models with one functional covariate, we extend our approach to multiple functional covariates and discuss simplifications exploiting the Tucker decomposition's nonsingular transformation indeterminacy. We consider convex penalty functions that, unlike previous approaches, directly regularize the estimated tensor effect through the assumed structure rather than only its decomposition parameters. We establish theoretical properties for the proposed model, including global, local, and approximation convergence for the proposed algorithm and, using empirical process theory, asymptotic statistical results regarding estimator consistency and normality. Finally, we demonstrate the performance of our model in simulated and real-world settings. Through a simulation study proposed in previous works that attempt to recover image signals of various geometric shape, we highlight the superiority of quantile-based methods for heavy-tailed error distributions. We examine the effect of tensor decomposition rank, quantile level, signal-to-noise ratio, and sample size on model estimates, further improving signal recovery by using a LASSO-type penalty. Second, we apply our methods to a real-world neuroimaging dataset from the Alzheimer's Disease Neuroimaging Initiative. Our model relates clinical covariates and and four functional covariates obtained from magnetic resonance imaging scans to mini-mental state examination score, a screening tool for Alzheimer's disease. After LASSO regularization leaves more be desired in estimate interpretability, we explore fused LASSO penalization to enforce estimate smoothness in a post-hoc analysis. Results show improvement that would not be possible with previous work through direct penalization of decomposition parameters. The major work in this thesis fills the need for an extension of existing functional quantile methods to tensor and high-dimensional functional data. Our results furthermore address the practical issue of multiple functional covariates---typically ignored in other work---and demonstrate the utility of direct regularization in tensor effect interpretability for imaging data.

This work develops Bayesian spatio-temporal modeling techniques specifically aimed at studying several aspects of our motivating applications, to include vector-borne disease incidence and air pollution levels. A key attribute of the proposed techniques are that they are scalable to extremely large data sets which consist of spatio-temporally oriented observations. The scalability of our modeling strategies is accomplished in two primary ways. First, through the introduction of carefully constructed latent random variables we are able to develop Markov chain Monte Carlo (MCMC) sampling algorithms that consist primarily of Gibbs steps. This leads to the fast and easy updating of the model parameters from common distributions. Second, for the spatio-temporal aspects of the models, a novel sampling strategy for Gaussian Markov random fields (GRMFs) that can be easily implemented (in parallel) within MCMC sampling algorithms is used. The performance of the proposed modeling strategies are demonstrated through extensive numerical studies and are further used to analyze vector-borne disease data measured on canines throughout the conterminous United States and PM 2.5 levels measured at weather stations throughout the Eastern United States. In particular, we begin by developing a Poisson regression model that can be used to forecast the incidence of vector-borne disease throughout a large geographic area. The proposed model accounts for spatio-temporal dependence through a vector autoregression and is fit through a Metropolis-Hastings based Markov chain Monte Carlo (MCMC) sampling algorithm. The model is used to forecast the prevalence of Lyme disease (Chapter 2) and Anaplasmosis (Chapter 3) in canines throughout the United States. As a part of these studies we also evaluate the significance of various climatic and socio-economic drivers of disease. We then present (Chapter 4) the development of the 'chromatic sampler' for GMRFs. The chromatic sampler is an MCMC sampling technique that exploits the Markov property of GMRFs to sample large groups of parameters in parallel. A greedy algorithm for finding such groups of parameters is presented. The methodology is found to be superior, in terms of computational effort, to both full block and single-site updating. For assessing spatio-temporal trends, we develop (Chapter 5) a binomial regression model with spatially varying coefficients. This model uses Gaussian predictive processes to estimate spatially varying coefficients and a conditional autoregressive structure embedded in a vector autoregression to account for spatio-temporal dependence in the data. The methodology is capable of estimating both widespread regional and small scale local trends. A data augmentation strategy is used to develop a Gibbs based MCMC sampling routine. The approach is made computationally feasible through adopting the chromatic sampler for GMRFs to sample the spatio-temporal random effects. The model is applied to a dataset consisting of 16 million test results for antibodies to Borrelia burgdoferi and used to identify several areas of the United States experiencing increasing Lyme disease risk. For nonparametric functional estimation, we develop (Chapter 6) a Bayesian multidimensional trend filter (BMTF). The BMTF is a flexible nonparameteric estimator that extends traditional one dimensional trend filtering methods to multiple dimensions. The methodology is computationally scalable to a large support space and the expense of fitting the model is nearly independent of the number of observations. The methodology involves discretizing the support space and estimating a multidimensional step function over the discretized support. Two adaptive methods of discretization which allows the data to determine the resolution of the resulting function is presented. The BMTF is then used (Chapter 7) to allow for spatially varying coefficients within a quantile regression model. A data augmentation strategy is introduced which facilitates the development of a Gibbs based MCMC sampling routine. This methodology is developed to study various meteorological drivers of high levels of PM 2.5, a particularly hazardous form of air pollution consisting of particles less than 2.5 micrometers in diameter.

There is a paucity of research examining the skills that contribute to reading comprehension for adults who struggle with reading, which includes one in six adults in the United States (Organisation for Economic Co-operation and Development, 2013). The current studies addressed some of the gaps in this literature. Study 1 explored the Simple View of Reading (SVR), which postulates that reading comprehension is predicted by two component skills: decoding and linguistic comprehension (Gough & Tunmer, 1986). Participants included 392 struggling adult readers who were native speakers of English. The dimensionality of the SVR components was examined using confirmatory factor analysis. For the decoding component, a parsimonious latent representation inclusive of phonic decoding and word recognition provided good fit to the data. With respect to linguistic comprehension, the subcomponents of oral vocabulary and listening comprehension emerged as separable yet highly related constructs. A structural equation model showed that decoding and listening comprehension made significant unique contributions to reading comprehension, whereas oral vocabulary did not emerge as a significant unique predictor. Additionally, quantile regression analyses indicated that decoding, listening comprehension, and oral vocabulary exhibited significant unique effects on reading comprehension at low, average, and high levels of reading comprehension performance (.10, .50, and .90 quantiles), with decoding making the largest unique contributions. Study 2 examined the influence of decoding, oral vocabulary, fluency, listening comprehension, background knowledge, and inferencing across different reading comprehension tests. Participants included 168 struggling adult readers who were native speakers of English. The explanatory effects of the predictors were estimated for three reading comprehension tests: WJ Passage Comprehension (WJ-PC), RISE Reading Comprehension (RISE-RC), and RAPID Reading Comprehension (RAPID-RC). Ordinary least squares regression analyses indicated that all predictors except for listening comprehension uniquely explained variance in WJ-PC scores, whereas significant unique predictors were limited to decoding and listening comprehension for RAPID-RC and only decoding for RISE-RC. Quantile regression analyses indicated that the effects of oral vocabulary and background knowledge differed across levels of WJ-PC performance, the effects of decoding and listening comprehension differed across levels of RAPID-RC performance, and the effect of decoding was stable across levels of RISE-RC performance.

Marketing value assessment, the identification and measurement of marketing’s influence on firm performance, is a challenging, yet imperative undertaking as marketing managers are under increasing pressure to defend the value of their activities (Hanssens and Pauwels 2016; Morgan 2012). These activities necessitate financial resource allocations that trickle down from larger strategic marketing investment decisions (Hanssens and Pauwels 2016). However, these allocation efforts are often managed separately in functional “silos” within firms (Hanssens and Pauwels 2016; Keiningham, Aksoy, Perkins-Munn and Vavra 2005), potentially leading to ineffectiveness and inefficiencies of marketing resource allocations. Surprisingly, very little is known about the quantifiable issues associated with managing specific marketing assets and resource allocations within organizational silos and the implications for marketing managers (Keiningham et al. 2005).In this dissertation, I examine the effects of resource allocations, and specifically, the importance of cross-functional and strategic integration, on marketing performance indicators. In my first essay, I investigate marketing resource allocations through two fundamental processes, value creation and value appropriation, across two strategic dimensions, internally versus via interfirm relationships. In my second essay, I investigate potential spillover benefits from marketing resource allocations to customer satisfaction and brand equity. Using a theoretical resource orchestration and a marketing capabilities framework, I promote the importance of breaking down organizational silos at different hierarchical levels to enhance marketing resource allocation effectiveness and efficiencies.

Fama-French three factors asset pricing model has been well documented for the stock market cross the world. This research will apply Fama-French model to Chinese stock market using the quantile regression approach. All the portfolios are sorted by size and book-to-market ratio to mimic the market size factor and market value factor. The regression reveal that portfolios returns are positively related with market risk and investors will make more profit by holding stocks with smaller company size and higher book-to-market ratio. With the assumption that the returns are normally distributed and expected returns are linearly dependent on three factors, existing studies on Chinese stock market have used ordinary least square (OLS) method to test asset pricing models. These assumptions are not valid in most of the markets. Thus, the present study tests the three risk factors model using quantile regression with the same data set. The results of the study reveal that the when it comes to extreme values in a distribution, the OLS method becomes inefficient. Quantile regression is a better way for investors to examine the extreme values in the distribution tails.

The significance of this dissertation research is twofold with both methodological advancement and empirical update. In this dissertation research, quantile regression (QR) was introduced to social sciences researchers as a response to the weaknesses of the traditional mean-based regression often referred to as multiple regression. General advantages of QR includes being more flexible for modeling data with heterogeneous conditional distributions, more robust to outliers, and having richer characterization and description of the data. Results of QR allow researchers to not only describe a general trend of changes in the effects of the independent variables across a continuous distribution of the dependent variable but also provide information on characteristics of any shift in the distribution caused by the independent variables. These shifts pertain to location, scale, and shape shifts. This dissertation research reviewed graphical ways to examine location, scale, and shape shifts, and more importantly, developed statistical ways to quantify location, scale, and shape shifts (i.e., test for statistical significance of location, scale, and shape shifts). Overall, this dissertation demonstrated that the introduction of QR as an advanced statistical procedure will advance the quantitative landscape of social sciences research. The results of this dissertation showed that QR can detect the differential effects of independent variables on the dependent variables that mean-based regression cannot detect and therefore uncovers more detailed relationships. This quality of QR enables more in-depth research than mean-based regression in many fields. The results of this dissertation also showed that QR allows for the understanding of relationships between variables outside the mean of the data, making it useful in understanding outcomes that are non-normally distributed and that have non-linear relationships with the independent variables. Finally, this dissertation introduced ways to detect and describe distributional shifts caused by the independent variables. The median regression line describes the (central) location shift. In addition to the estimated location shifts, the other QR lines provide information about the scale and shape shifts. This dissertation developed the bootstrapping approach to test for statistical significance when comparing location, scale, and shape shifts between parameters within and between samples (i.e., studies). This dissertation research applied QR to the examination of individual differences in mathematics achievement and mathematics self-efficacy, using the 2003 and 2012 Programme for International Student Assessment (PISA) data. The QR results showed that the effects of many student characteristics were not constant across the mathematics outcomes distributions (i.e., mathematics achievement and mathematics self-efficacy). This suggested that individual differences were valued heterogeneously across the mathematics outcomes distributions. There was only one statistically significant location shift in terms of individual differences associated with family structure in both mathematics achievement and mathematics self-efficacy between 2003 and 2012. There was only one statistically significant scale shift in terms of individual differences associated with father SES in mathematics achievement for the middle 40 percent of the students between 2003 and 2012. There was only one statistically significant scale shift in terms of individual differences associated with gender in mathematics self-efficacy for the middle 40 percent of the students between 2003 and 2012. There was only one statistically significant shape shift in terms of individual differences associated with gender in mathematics self-efficacy between 2003 and 2012. Even though QR and LMR results can be similar in terms of statistical significance, they can differ dramatically in magnitude. Students’ age, gender, and socioeconomic status were typical examples in this study. The effect of student age generally became more positive as student mathematics achievement increased in 2003. This suggests that age had a stronger effect on better-performing students than lower-performing students in 2003. It also means that there are more age differences in the upper tail of student mathematics achievement distribution than in the lower tail.

Consequent to developed and liberalized financial markets in emerging market economies, the magnitude of gross capital outflows is getting larger. My dissertation focuses on massive foreign asset purchases by domestic agents which is called capital flight and the study aims to see new empirical evidence on its impact and determinants and the associations between it and other macro variables using diverse methods in econometrics. In particular, I am interested in its role in emerging market economies since they are especially vulnerable to such large and unexpected capital flows. First chapter investigates the impact of capital flight on domestic countries' real GDP growth and investment. Specifically, it employs diverse GMM estimators (difference, system, and orthogonal deviation GMM) to estimate their causal effects and uses interaction models to test the hypothesis that the effect of flights is conditional on the amount of external loans (gross capital inflows) in the country. The results show that flights are harmful only if there are not enough external loans and, otherwise, they fail to depress domestic economies. They are contrasted with those of capital inflow stops, which consistently decrease growth and, therefore, indicate inflow stops and outflow flights are different phenomena. Second chapter estimates the impacts of domestic private saving and gross capital inflows on gross capital outflows in 56 emerging market economies over 1990 - 2014 using Powell's (2015) quantile regression methodology. The purpose is to test two hypotheses: first, capital outflows are mostly fueled by capital inflows rather than by domestic saving and, second, the causal impact of capital inflows is stronger in the upper quantiles of capital outflows. According to the result, the response of capital outflows to capital inflows and domestic saving is similar if capital outflows are below the median. However, if they are above the median, the impact of external loans is stronger than that of saving. Furthermore, a country tends to borrow from foreign countries to purchase debts rather than equities in the short run. It is consistent with several stylized facts such as pro-cyclical capital inflows and outflows and high leverage ratio and high probability of serial default and sudden stops during short-term booms.Third chapter studies the association between extreme gross capital outflow movements (flight and retrenchment) and diverse financial crises (banking, currency, debt, and inflation crises) in 60 emerging markets between 1980 and 2009. Considering that the movements reflect domestic agents' strong preferences for (against) foreign assets, domestic turmoil might have affected or conversely been triggered by their behavior. In either case, large capital outflows are associated with crises and provide valuable information to both foreign interests and domestic policymakers. Results from the complementary log-log model show, first, that banking, currency, and inflation crises are associated with capital flight; second, debt crises are also associated with capital flight, but the result is not robust to different specifications; third, the positive association between capital flight and crises is mainly driven by banking flows rather than FDI and portfolio flows; and finally, capital retrenchment is not associated with any kind of crisis. The results support several arguments addressed in the existing literature, including the ``flight-to-safety" hypothesis and the self-fulfilling prophecy.

Nonparametric modeling tends to capture the underlying structures in the data without imposing strong model assumptions. The nonparametric estimation provides powerful data-driven approaches to fit a flexible model to the data. Single-index models are useful and appealing tools to preserve the flexibility and interpretability but to overcome “curse of dimensionality” problems in nonparametric regression. In this dissertation, we consider partially linear single-index models for quantile regression. This set of semi-parametric models allow some of covariates in linear form and other covariates in nonparametric term to reflect the non-linear feature in modeling the conditional quantiles of the response variable. We first develop efficient estimation and variable selection for partially linear single-index quantile models in the fixed dimension. We use spline smoothing with B-spline basis to estimate the nonparametric component and adopt the non-convex penalties to select variables simultaneously. We study the theoretical properties of the resulting estimators and establish the “oracle property” for penalized estimation. With the rise of new technologies used in data collection and storage, high dimensional data spring up and become available in various scientific fields. Often researchers face the new challenge that the dimension of the explanatory variables, p, may increase with the sample size, n, or potentially become much larger than n. For those problems of high to ultra-high dimensionality, data are likely to be heterogeneous and the underlying model is prone to be nonlinear. Variable selection will also play a critical role in the dimension reduction and modeling process. Thus, we propose a penalized estimation under the sparsity assumption for partially linear single-index quantile models in high dimension. We further investigate ultra-high dimensional penalized partially linear single-index quantile models in which both linear components and single-index variables in nonparametric term can be in high to ultra-high dimension. Both the numerical studies and the real data applications demonstrate that the proposed models and variable selection procedure work very well, even for data in ultra-high dimensionality.

Quantile Regression Model (QRM), introduced by Koenker and Bassett in 1978, is a well-established and widely used technique in theoretical and applied statistics. QRM is a natural extension of the traditional OLS regression model and it is advantageous over the traditional techniques in several aspects: (1) QRM is robust to outliers, non-normal errors and heteroscedasticity; (2) It allows researchers to study the impact of predictors on different quantiles of response variable, not merely its conditional mean. Due to these advantages, QRM is applied in various fields such as risk measurement in finance, and fat-tailed distributions such as if cheaper food cause obesity. The current research paper aims at applying QRM in an open source housing data with 79 house-related features and 1460 cases, and comparing its predictive performance with the OLS model. The article also extends the QRM to Bayesian Quantile Regression and Quantile Random Forest to further explore the application performance of quantile models. The results indicate that all the quantile models outperformed the OLS regression in prediction at the 0.5th quantile and the 0.75th quantile based on RMSE. In general, most estimates derived by QRM and BQR show consistency across quantiles. Quantile Random Forest show similar variable selection results comparing with LASSO, but slightly higher RMSE than the other quantile models.

This dissertation consists of two chapters on the industrial organization of mortgage markets in the United States.In the first chapter, titled “Consumer Search Costs in U.S. Mortgage Markets”, I focus on estimating the distribution of consumer search costs in the market for government-backed mortgages in the US during the period from September 2013 to March 2015. I adapt the Hortaçsu and Syverson (2004) search model to mortgage markets. I estimate the distribution of consumer search costs in each U.S. state using recent data on government-insured mortgages. I find that estimated search costs are large; a median borrower would face a search cost equivalent to about $40 in monthly repayment. At the state-level, search cost magnitude is related positively to household income and age and negatively to years of education. I solve counterfactual scenarios in order to study the relationship between search costs and welfare. Compared to the full information scenario, the presence of costly consumer search decreases social welfare by about $600 in monthly repayment per borrower. This decrease in welfare occurs because under costly search borrowers are matched with lower quality lenders and spend resources on searching. At the national level, this decrease corresponds to approximately $35 million per-month. Reductions in search costs would raise social welfare monotonically. A 10% reduction in search cost may raise social welfare by as much as $130 per borrower per month. These findings support recent policies that aim to reduce search costs of mortgage borrowers. In the second chapter, titled “Price Discrimination in U.S. Mortgage Markets”, I examine the existence of price discrimination generated by costly consumer search in the market for mortgages. I develop a stylized model of consumer search in mortgage markets where firms charge optimal prices that depend on borrowers' search cost level. The model produces testable restrictions on the conditional quantile function of observed transacted rates. Using the data on insured Federal Housing Agency loans where price variation is not driven by default risk, I run a quantile regression of transacted interest rates on a set of loan observables, including borrower's credit score, original principal balance, and loan-to-value ratio, among others. I find that predictions of the theoretical model are satisfied for all loan observables under consideration, and price discrimination created by costly consumer search is likely to exist in U.S. mortgage markets.

In this dissertation we develop theory for inference and uncertainty quantification for potentially misspecified quantile regression processes when the number of predictor variables increases with or exceeds the sample size. Potential misspecification of the fitted model is a fundamental problem in statistics which is exacerbated by today's high-dimensional datasets, and quantile regression is often used in complex situations in which misspecifications are highly likely. We make the following contributions: First, we establish a uniform-in-model strong Bahadur representation for misspecified quantile regression processes when the number of predictor variables increases and provide tight error bounds on its remainder term which hold uniformly over growing collections of quantile regression functions. Second, we derive an almost sure de-biased representation of the Lasso-penalized high-dimensional misspecified quantile regression process and analyze the theoretical properties of the misspecified post-Lasso quantile regression estimator. Third, to quantify the uncertainty associated with a misspecified quantile regression function we analyze its predictive risk and expected optimism. We propose uniformly consistent estimators for both quantities when the number of regression functions is growing moderately with the sample size. Empirical evidence shows that our estimators perform favorably against cross-validation estimates. Forth, we develop a set of new exponential and maximal inequalities which allow to control the fluctuations of a collection of suprema of empirical processes over classes of unbounded functions when both the collection of function classes and the complexity of each individual the function class grow with the sample size. These new inequalities are instrumental in deriving the theoretical results in this dissertation.

Design flood estimates are needed for the planning and design of hydraulic structures, and in many other water and environmental management tasks. Design flood estimation is a challenging task, in particular for poorly gauged and ungauged catchments. In Australia, there are numerous ungauged catchments; for these catchments Regional Flood Frequency Analysis (RFFA) techniques are generally adopted to estimate design floods. Most of the RFFA techniques previously adopted in Australia are based on rational method and/or linear modelling approaches. However, with the recent advancements in statistical computation methods, there are several other techniques becoming popular gradually in hydrological applications which can account for non-linearity in the rainfall-runoff processes. Generalized additive model (GAM) is one of the recently developed techniques which can deal with the non-linearity, which has not been widely explored in hydrological research, in particular for the RFFA problems. Therefore, this research is devoted to examining the applicability of GAM in RFFA and compare its performances with one of the most widely used linear RFFA technique (log-log linear model). This study is carried out using data from 114 small to medium sized gauged catchments of Victoria, Australia. This data has primarily been sourced from Australia Rainfall Runoff (ARR), Project 5 Regional Flood Methods. This study is based on a number of alternative groups, e.g. a combined group consisting of all the 114 catchments and sub-groups formed based on cluster analysis. Four regions are formed using hierarchical and k-means clustering techniques. All the five groups are used for developing log-log linear models and GAM based models. The predictor variables for each of these models are selected based on the statistical significance of the predictor variables, i.e. p-statistics. For validation of the developed prediction models, a 10-fold cross validation method is adopted. The performances of the prediction models for the alternative models are assessed using a number of statistical measures including coefficient of determination (R2), median relative error (RE) and median Qpred/Qobs ratio values. It is found that, none of the models from the combined group and clustering groups perform equally well for the six average recurrence intervals (ARIs) (2, 5, 10, 2, 50 and 100 years) with respect to the selected statistical measures. Overall, log-log linear model from clustering group A1 is found to be the best performing model. GAM based RFFA models perform better for smaller ARIs (i.e., 2, 5 and 10 years); which is as expected since the hydrological behaviour of catchments for smaller ARIs is generally more non-linear, e.g. higher loss and hence rainfall produces lower runoff for more frequent events. Some predictor variables (e.g., evap), which were not adopted in the previous RFFA models, in Australia are found to be significant in the GAM based RFFA models. Overall, it is found that consideration of non-linearity via GAM can add new dimensions in RFFA modelling for selecting appropriate predictor variables and to deal with non-linearity. Overall, the results of this study demonstrate that GAM has a strong potential to enhance the accuracy of RFFA models in Australia; however, additional predictor variables are needed (than what are included in this study) to capture the non-linearity more explicitly between runoff and flood producing variables.

Tested in Texas savannas of a wide rainfall gradient, this dissertation endeavors to (1) map fractional woody cover at Landsat scale, for close and continuous woody plant encroachment monitoring, (2) model the pattern of potential woody cover over the present rainfall gradient, for implication of the end-point of woody plant encroachment, (3) analyze the rate and effect factors of woody plant encroachment under the regional context, for pertinent savanna management strategy. Web-Enabled Landsat Data (WELD) was used to calibrate the Salford Systems’ Classification and Regression Trees (CART) against training data of fractional woody cover derived from 1m resolution digital orthophotos. The CART model output was verified against an independent test data. This study provides a way to accurately monitor woody plant encroachment across savanna ecosystems at a fine spatial scale, and sets up a protocol for landscape components mapping at sub-pixel level in other ecosystems. The pattern of potential woody cover was modelled over the wide rainfall gradient at Landsat scale (30m) and MODIS scale (500m) respectively. While a positive linear relationship between potential woody cover and mean annual precipitation (MAP) was revealed at Landsat scale, a prominent three-segment relationship was observed at MODIS scale. This discrepancy corroborates the scale dependency of the primary determinants of savanna woody plant density. According to the three-segment pattern at MODIS scale, Texas savannas are divided into arid savanna (MAP < 600mm), semi-arid savanna (600mm < MAP < 735mm), and mesic savanna (MAP > 735mm). Analysis of the encroachment of Ashe juniper at its early life stage (initial ~20 years) at local (hectare) scale suggests that water availability has a significant positive effect on the encroachment rate in semi-arid savanna, but not in mesic savanna. In addition, a quadratic relationship was revealed between the encroachment rate and woody plant density in mesic savanna. That is, the encroachment rate increases with woody plant density by a threshold density, then starts decreasing with woody plant density. These results demonstrate that regional context such as rainfall and biological traits of woody species is critical to understand the trend of woody plant encroachment.

Abstract: In this thesis, we study the partial quantile regression methods in functional data analysis. In the first part, we propose a prediction procedure for the functional linear quantile regression model by using partial quantile covariance techniques and develop a simple partial quantile regression (SIMPQR) algorithm to efficiently extract partial quantile regression (PQR) basis for estimating functional coefficients. In the second part, we propose and implement an alternative formulation of partial quantile regression (APQR) for functional linear model by using block relaxation ideas and finite smoothing techniques. Such reformulation leads to insightful results and motivates new theory, demonstrating consistency and establishing convergence rates by applying advanced techniques from empirical process theory. In the third part, we propose and implement the generalization of PQR procedure to multidimensional functional linear model using tensor decomposition techniques. We also establish and demonstrate the corresponding asymptotic properties. In all three parts, extensive simulations and real data are investigated to show the superiority of our proposed methods, while the advantages of our proposed PQR basis are well demonstrated in various settings for functional linear quantile regression model.

Massive and complex data present new challenges that conventional sparse penalized mean regressions, such as the penalized least squares, cannot fully solve. For example, in high-dimensional data, non-constant variance, or heteroscedasticity, is commonly present but often receives little attention in penalized mean regressions. Heavy-tailedness is also frequently encountered in many high-dimensional scientific data. To resolve these issues, unconventional sparse regressions such as penalized quantile regression and penalized asymmetric least squares are the appropriate tools because they can infer the complete picture of the entire probability distribution. Asymmetric least squares regression has wide applications in statistics, econometrics and finance. It is also an important tool in analyzing heteroscedasticity and is computationally friendlier than quantile regression. The existing work on asymmetric least squares only considers the traditional low dimension and large sample setting. We systematically study the Sparse Asymmetric LEast Squares (SALES) under high dimensionality and fully explore its theoretical and numerical properties. SALES may fail to tell which variables are important for the mean function and which variables are important for the scale/variance function, especially when there are variables that are important for both mean and scale. To that end, we further propose a COupled Sparse Asymmetric LEast Squares (COSALES) regression for calibrated heteroscedasticity analysis. Penalized quantile regression has been shown to enjoy very good theoretical properties in the literature. However, the computational issue of penalized quantile regression has not yet been fully resolved in the literature. We introduce fast alternating direction method of multipliers (ADMM) algorithms for computing penalized quantile regression with the lasso, adaptive lasso, and folded concave penalties. The convergence properties of the proposed algorithms are established and numerical experiments demonstrate their computational efficiency and accuracy. To efficiently estimate coefficients in high-dimensional linear models without prior knowledge of the error distributions, sparse penalized composite quantile regression (CQR) provides protection against significant efficiency decay regardless of the error distribution. We consider both lasso and folded concave penalized CQR and establish their theoretical properties under ultrahigh dimensionality. A unified efficient numerical algorithm based on ADMM is also proposed to solve the penalized CQR. Numerical studies demonstrate the superior performance of penalized CQR over penalized least squares under many error distributions.

The dissertation is focused on the analysis of economic forecasting with a large number of predictors. The first chapter develops a novel forecasting method that minimizes the effects of weak predictors and estimation errors on the accuracy of equity premium forecasts. The proposed method is based on an averaging scheme applied to quantiles conditional on predictors selected by LASSO. The resulting forecasts outperform the historical average, and other existing models, by statistically and economically meaningful margins. In the second chapter, we find that incorporating distributional and high-frequency information into a forecasting model can produce substantial accuracy gains. Distributional information is included through a quantile combination approach, but estimation of quantile regressions with mixed-frequency data leads to a parameter proliferation problem. We consider extensions of the MIDAS and soft (hard) thresholding methods towards quantile regression. Our empirical study on GDP growth rate reveals a strong predictability gain when high-frequency and distributional information are adequately incorporated into the same forecasting model. The third chapter analyzes the wage effects of college enrollment for returning adults based on the NLSY79 data. To improve the estimation efficiency, we apply the double-selection model among time-varying features and individual fixed effects. The empirical results on hourly wage predictions show evidences towards the superiority of double-selection model over a fixed-effect model. Based on the double-selection model, we find significant and positive returns on years of college enrollment for the returning adults. On average, one more year's college enrollment can increase hourly wage of returning adults by $1.12, an estimate that is about 7.7% higher than that from the fixed-effect model.

Abstract: There is an increasing interest in extreme value analysis for financial and climate data. Various statistical methods have been developed for estimating extreme value dependence in time series data sets and the field continues to grow. In this work we consider four statistical methods for estimating extreme value dependence: the extremogram and cross extremogram, quantile regression, the cross-quantilogram and the upper tail dependence coefficient estimated using Gumbel copulas. We consider within series dependence but also cross serial dependence which may be of more interest. We compare the four methods using a data set of spot electricity prices from Australian states included in the National Electricity Market. In addition we discuss the advantages and disadvantages of each method. Finally, a freeware R package, "extremogram", is made available that implements the extremogram methods.

This dissertation consists of three essays on the application of Transformed Ordinal Quantile Regression (TORQUE) developed by Hong and He (2010). TORQUE is based on jittered response, a nonparametric link function, a semiparametric quantile estimation. When the response variable is categorical an application of the standard quantile regression is not optimal. TORQUE technique generalizes ordinary quantile regression, and as a semiparametric method it is more robust than Maximum Likelihood Estimators. In the first essay I estimate conditional quantiles of happiness using the data from British Household Panel Survey (BHPS) for 2006. I find the continuity assumption of happiness ranking does not hold in this framework, implying the direct application of standard quantile regression could produce biased estimators. Results indicate that income, health, and social factors are very important across all quantiles but decreasing in their magnitude. Education has a significant negative association with happiness at upper quantiles and that females are generally happier than their male counterparts. The second essay tests an augmented quantity-quality model of fertility. I focus on the effect of Rosenwald schools on conditional quantiles of fertility for rural black women. Results roughly confirm the model. At the extensive margin, a better access to education increased the probability of having a child from 3.3 to 4.2 percent. I do not find significant effect along the extensive margin. However, OLS estimates infer large and significant negative effects. I also test the same theoretical model for a sample of women who could have attended Rosenwald schools themselves. I find that school exposure decreased the probability of having a child. Results confirm model predictions. The third essay examines the relationship between state medical marijuana laws and marijuana consumption among high school students. Unlike other papers we focus on the frequency of marijuana use rather than only on participation. Using frequency data allows to understand the relationship between MMLs and marijuana use for different demographics, such as light smokers vs. heavy smokers. Results imply that MMLs reduce the probability of smoking. This finding is consistent across different groups and estimators.

In recent years, penalized models have gained considerable importance on deal- ing with variable selection and estimation problems under high dimensional settings. Of all the candidates, the l1 penalized, or the LASSO model retains popular application in diverse fields with sophisticated methodology and mature algorithms. However, as a promising alternative of the LASSO, non-convex penalized methods, such as the smoothly clipped absolute deviation (SCAD) and minimax concave penalty (MCP) methods, produce asymptotically unbiased shrinkage estimates and owns attractive ad- vantages over the LASSO. In this thesis, we propose intact methodology and theory for multiple non-convex penalized models. The proposed theoretical framework includes estimator’s error bounds, oracle property and variable selection behaviors. Instead of common least square models, we focus on quantile regression and support vector ma- chines (SVMs) for exploration of heterogeneity and binary classification. Though we demonstrate current local linear approximation (LLA) optimization algorithm possesses those nice theoretical properties to achieve the oracle estimator in two iterations, the computation issue is highly challenging when p is large due to the non-smoothness of the loss function and the non-convexity of the penalty function. Hence, we also explore the potential of coordinate descent algorithms for fitting selected models, establishing convergence properties and presenting significant speed increase on current approaches. Simulated and real data analysis are carried out to examine the performance of non- convex penalized models and illustrate the outperformance of our algorithm in computational speed.

The dissertation consists of two distinct but related research projects. First of all, we study the Bayesian analysis on the two-piece location-scale models, which contain several well-known sub-distributions, such as the asymmetric Laplace distribution, the skewed normal distribution, and the skewed Student-t distribution. The use of two-piece location-scale models is an attractive method to model non-symmetric data. From a practical point of view, a prior with some objective information may be more reasonable due to the lack of prior information in many applied situations. It has been shown that several common used objective priors, such as the Jeffreys prior, result in improper posterior distributions for the case of two-piece location-scale models. This motivates us to consider alternative priors. Specifically, we develop reference priors with partial information which lead to proper posterior distributions. Based on those priors, we extend our prior to a general class of priors. A sufficient and necessary condition is provided to ensure the propriety of the posterior distribution under such general priors. Our results show that the proposed Bayesian approach outperforms the frequentist method in terms of mean squared error. It is noteworthy that the proposed Bayesian method can be applied to the quantile regression due to the close relationship between the asymmetric Laplace distribution and the quantile regression. The second project deals with the Bayesian variable selection for the maximum entropy quantile regression. Quantile regression has gained increasing popularity in many areas as it provides richer information than the regular mean regression, and variable selection plays an important role in quantile regression model building process, as it can improve the prediction accuracy by choosing an appropriate subset of regression predictors. Most existing methods in quantile regression consider quantile at some fixed value. However, if our purpose is, among all the fitted quantile regression models, to identify which one fits the data best, then the traditional quantile regression may not be appropriate. Therefore, we consider the quantile as an unknown parameter and estimate it jointly with other regression coefficients. In particular, we consider the maximum entropy quantile regression whose error distribution is obtained by maximizing Shannon's entropy measure subject to two moment constraints. We apply the Bayesian adaptive Lasso to the model and put a flat prior on the quantile parameter due to the lack of information on it. Our proposed method not only addresses the problem about which quantile would be the most probable one among all the candidates, but also reflects the inner relationship of the data through the estimated quantile. We develop an efficient Gibbs sampler algorithm and show that the results of our proposed method are better than the ones under the Bayesian Lasso and Bayesian adaptive Lasso with fixed quantile values through both simulation studies and real data analysis.

Abstract: Quantile, composite quantile regression with or without regularization have been widely studied and applied in the high-dimensional model estimation and variable selections. Although the theoretical aspect has been well established, the lack of efficient computation methods and publicly available programs or packages hinder the research in this area. Koenker has established and implemented the interior point(IP) method in quantreg for quantile regression with or without regularization. However, it still lacks the ability to handle the composite quantile regression with or without regularization. The same incapability also existed in Coordinate Descent (CD) algorithm that has been implemented in CDLasso. The lack of handful programs for composite quantile regression with or without regularization motivates our research here. In this work, we implement three different algorithms including Majorize and Minimize(MM), Coordinate Descent(CD) and Alternation Direction Method of Multiplier(ADMM) for quantile and composite quantile regression with or without regularization. We conduct the simulation that compares the performance of four algorithms in time efficiency and estimation accuracy. The simulation study shows our program is time efficient when dealing with high dimensional problems. Based on the good performance of our program, we publish the R package cqrReg, which give the user more flexibility and capability when directing various data analyses. In order to optimize the time efficiency, the package cqrReg is coded in C++ and linked back to R by an user-friendly interface.