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This dissertation covers topics in estimation and forecasting under structural breaks, intime-series and panel data models.Chapter two considers the linear structural breaks model with m breaks (m + 1regimes), and aim in improving the estimation of the parameters within each regime. Weform an optimal combined estimator of regression parameters based on combining restrictedestimator under the restriction of no breaks in the parameters, with unrestricted estimatorwhich considers the observations within each regime separately. We derive the analyticalfinite sample risk and asymptotic risk and show that the risk of the combined estimator isless than the unrestricted estimator. The simulation study and the empirical example offorecasting the U.S. output growth confirm our theoretical findings.Chapter three develops an optimal combined estimator to forecast out-of-sampleunder structural breaks. We propose the combined estimator of the post-break estimatorwith the full-sample estimator which uses all observations in the sample. Using a localasymptotic framework, we obtain the asymptotic risk for the combined estimator and showthat it is strictly less than the risk of the post-break estimator, which is a common solutionfor forecasting under structural breaks. We also introduce a semi-parametric estimator. Using a discrete kernel, this estimator assigns full weight of one to the post-break observationsand down-weights the pre-break sample observations. The kernel is found by cross validation. Simulation study and the empirical example of forecasting equity premium confirmour analytical findings.Chapter four proposes an efficient Stein-like shrinkage estimator for estimating theslope parameters in the heterogeneous panel data models with cross-sectional dependence.We combine the unrestricted estimator with the restricted one. The unrestricted estimatorestimates the parameters by considering the break points and only uses the observationswithin each regime, while the restricte

Since the introduction of the subject of econometrics, parametric functional forms of the relationship between independent and dependent variables are often assumed to be known. Econometric functions built from misspecified parametric assumptions may result in false estimation and invalid implications. For this dissertation I introduce an information theoretic (IT) approach to construct econometric functions based on minimal model assumptions on the variables. I follow the entropy approach initiated by Shannon (1948) to obtain a probability distribution of the variables through maximizing the entropy function. In Chapter 2, I use moment constraints to construct the IT-based maximum entropy density, regression and response functions, the performance of which is investigated through simulation and empirical examples. I demonstrate the maximum entropy econometric functions are purely date-driven, easy to implement and advantageous over parametric and nonparametric kernel methods. Furthermore, in Chapter 3, I extend the use of IT-based maximum entropy estimators to a time series dataset by incorporating a theoretic constraint.Based on the structure of IT-based estimators, the number of moment conditions increase rapidly with the growing dimensionality of variables. Computational burden of maximum entropy estimation with all the observed moments becomes heavier accordingly. Thus, I link the problem of IT-based maximum entropy estimation and moment selection in Chapter 4. We propose a regularized ME approach to select relevant moments. We also use the entropy ratio test to select moments of which the Lagrange multipliers are significant. Simulation examples show that the probability of selecting relevant moments approaches to one as sample size gets larger. Lastly, I explore the regularization of high dimensional matrices in Chapter 5. I deal with the challenge of estimating large precision matrices which are often used in a variety of applications. I propose a dynamic co

This dissertation covers topics in classification with high-dimensional data, variable selection in sparse semiparametric single-index models and statistical inference under heteroskedasticity. In particular, Chapter 1 provides the motivation and background of the dissertation.Chapter 2 provides a summary of boosting methods for classification, namely Discreet AdaBoost, Real AdaBoost, P-AdaBoost, Gentle AdaBoost and LogitBoost. We compare these methods with alternative machine learning classification tools such as Deep Neural Network and demonstrate the empirical applications in economics, such as prediction of business cycle turning points and directional prediction of stock price indexes.Chapter 3 generalizes the Discreet AdaBoost shown in Chapter 2 for binary classification problem with state-dependent loss functions. We introduce Asymmetric AdaBoost that solves the asymmetric maximum score problem with high-dimensional data. Asymmetric AdaBoost produces a nonparametric classifier via minimizing the ``asymmetric exponential risk'' which is a convex surrogate of the traditional non-convex score risk or 0-1 risk. The convex risk function gives huge computation advantage over non-convex risk functions, e.g. Maximum Score (Manski, 1975, 1985), especially when the data is high-dimensional.Chapter 4 considers the "Regularization of Derivative ExpectationOperator" (RODEO) of Lafferty and Wasserman (2008) and propose a modified RODEO algorithm for sparse semiparametric single-index models which we call the SIM-RODEO. The SIM-RODEO method is able to distinguish relevant explanatory variables from irrelevant variables and gives a competitive estimator for the model.In addition, the algorithm finishes in a reasonable period of time. In addition, the algorithm finishes in a reasonable period of time.Chapter 5 investigates the methods for statistical inference under the presence of heteroskedasticity of unknown form in the disturbances of linear regression models. We propose

This dissertation covers several topics in the second-order bias and mean squared error (MSE) of quantile and expectile estimators.Chapter one presents the introduction of this dissertation. Thefinite sample theory using higher order asymptotics provides better approximations of the bias and MSE for a class of estimators. Rilstone, Srivastava and Ullah (1996) provided the second-order bias results of conditional mean regression. The goal of this dissertation is to develops analytical results on the second-order bias and MSE for quantile and expectile estimators.Chapter two develops new analytical results on the second-order bias up to order O(N^-1) and MSE up to order O(N^-2) of the conditional quantile regression estimators. First, we provide the general results on the second-order bias and MSE of conditional quantile estimators. The second-order bias result enables an improved bias correction and thus to obtain improved quantile estimation. In particular, we show that the second-order bias are much larger towards the tails of the conditional density than near the median, and therefore the benet of the second order bias correction is greater when we are interested in the deeper tail quantiles, e.g., for the study of income distribution and financial risk management. The higher order MSE result for the quantile estimation also enables us to better understand the sources of estimation uncertainty. Next, we consider three special cases of the general results, for the unconditional quantile estimation, for the conditional quantile regression with a binary covariate, and for the instrumental variable quantile regression (IVQR). For each of these special cases, we provide the second-order bias and MSE to illustrate their behavior which depends on certain parameters and distributional characteristics. The Monte Carlo simulation indicates that the bias is larger at the extreme low and high tail quantiles, and the second-order bias corrected estimator has better behavior th

This dissertation covers several topics in estimation and forecasting in panel data models.Chapter one considers the panel data model with correlated individual effects and regressors. We form a combined estimator from combining the fixed effects (FE) and random effects (RE) estimators. We derive the asymptotic distribution and the asymptotic risk of our estimator using a local asymptotic framework. We show that if the regressor dimension exceeds two, the asymptotic risk of the combined estimator is strictly less than that of FE estimator. Our simulation result shows that thecombined estimator can reduce finite sample MSE relative to the FE estimator for all degrees of endogeneity and heterogeneity, as well as relative to the RE estimator for moderate to large degrees of endogeneity and heterogeneity. We also apply the combined estimator to revisit the relationship between public capital infrastructure and private economic performance.Chapter two extends chapter one into the semi-parametric (SP) framework, and proposes a combined SP-FE and SP-RE estimator.Chapter three considers the panel data model with correlated residuals and regressors. In the presence of such correlation, both FE and RE estimators yield biased and inconsistent estimates of the parameter. We propose a combined FE and FE-2SLS estimator, and a combined RE and RE-2SLS estimator.Chapter four considers regression models for panel data that exhibit cross-section dependence due to common shocks. Model with factor structures for errors and regressors are considered. In this case, the FE estimator is inconsistent. To solve this problem, Pesaran (2006) introduced the common correlated effects pooled (CCEP) estimator. We propose a combined FE and CCEP estimator, and show that under certain conditions, the combined estimator has strictly smaller risk than the CCEP estimator. Finally, we use Holly et al. (2010) state-level housing data to show the applicability of the combined estimator.Chapter five proposes a comb

This dissertation covers several topics in estimation and forecasting in time series models. Chapter one is about estimation and feasible conditional forecasts properties from the predictive regressions, which extends previous results of OLS estimation bias in the predictive regression model by considering predictive regressions with possible zero intercepts, and also allowing the regressor to follow either a stationary AR(1) process or unit root process. The main thrust of this chapter is to develop an analytical bias reduced estimator and study the mean squared error (MSE) efficiency of the estimator. Then we investigate whether this estimation bias can lead to biased feasible forecasts conditional on the available sample observations, in addition to the expression of the mean squared forecast error (MSFE). The results from this chapter shed lights on the bias reduction estimator of the predictive regressions and its MSE properties in finite samples, as well as the optimal forecasts efficiency. We apply our analytical results to both simulated and financial data with financial return prediction using variables such as dividend yield and short rate. Results show that our bias reduction works well in estimation even when the data are skewed and having fat tails, and moreover, the bias reduced estimator improves out-of-sample forecasts. All of the results highlight the importance of the bias reduction in estimation and forecasting.Chapter two explores finite sample bias of the estimators in the first order autoregressive moving average model under a general error distribution. Since the quasi maximum likelihood estimator (QMLE) of parameters in thefirst order autoregressive moving average model (ARMA(1, 1)) can be biased in finite samples, this chapter discusses bias properties of the QMLE of the ARMA(1,1) model up to order $O(T^{-1})$ by applying the stochastic expansion and the formula and sheds light on the bias correction for the parameter estimation in applied w