Search

The policy relevant treatment effect (PRTE) measures the average effect of switching from a status-quo policy to a counterfactual policy under consideration. Estimation of the PRTE involves estimation of multiple preliminary parameters, including propensity scores, conditional expectation functions of the outcome and covariates given the propensity score, and marginal treatment effects. These preliminary estimators can affect the asymptotic distribution of the PRTE estimator in complicated and intractable manners. In this light, we propose an orthogonal score for double debiased estimation of the PRTE, whereby the asymptotic distribution of the PRTE estimator is obtained without any influence of preliminary parameter estimators as far as they satisfy mild requirements of convergence rates. To our knowledge, this paper is the first to develop limit distribution theories for inference about the PRTE.

Policy evaluation is central to economic data analysis, but economists mostly work with observational data in view of limited opportunities to carry out controlled experiments. In the potential outcome framework, the panel data approach (Hsiao, Ching and Wan, 2012) constructs the counterfactual by exploiting the correlation between cross-sectional units in panel data. The choice of cross-sectional control units, a key step in its implementation, is nevertheless unresolved in data-rich environment when many possible controls are at the researcher's disposal. We propose the forward selection method to choose control units, and establish validity of the post-selection inference. Our asymptotic framework allows the number of possible controls to grow much faster than the time dimension. The easy-to-implement algorithms and their theoretical guarantee extend the panel data approach to big data settings., Comment: accepted for publication at the Journal of Econometrics

This paper considers a treatment effect model in which individual treatment effect may be heterogeneous, even among observationally identical individuals. Specifically, by extending the classical instrumental-variables (IV) model with an endogenous binary treatment, the heteroskedasticity of the error disturbance is allowed to vary with the treatment variable so that the treatment generates both mean and variance effect on the outcome. In this endogenous heteroskedasticity IV (EHIV) model, the standard IV estimator can be inconsistent for the average treatment effect (ATE) and lead to incorrect inference. After nonparametric identification is established, closed-form estimators are provided under the linear EHIV specification for the mean and variance treatment effect, as well as the average treatment effect on the treated (ATT). Asymptotic properties of the estimators are derived. We use Monte Carlo experiments to investigate the performance of the proposed approach and then consider an empirical application regarding the effect of fertility on female labor supply. Our findings demonstrate the importance of accounting for endogenous heteroskedasticity.

When predicting crop yield using both functional and multivariate predictors, the prediction performances benefit from the inclusion of the interactions between the two sets of predictors. We assume the interaction depends on a nonparametric, single-index structure of the multivariate predictor and reduce each functional predictor’s dimension using functional principal component analysis (FPCA). Allowing the number of FPCA scores to diverge to infinity, we consider a sequence of semiparametric working models with a diverging number of predictors, which are FPCA scores with estimation errors. We show that the parametric component of the model is root-n consistent and asymptotically normal, the overall prediction error is dominated by the estimation of the nonparametric interaction function, and justify a CV-based procedure to select the tuning parameters.

Change point detection in time series has attracted substantial interest, but most of the existing results have been focused on detecting change points in the time domain. This paper considers the situation where nonlinear time series have potential change points in the state domain. We apply a density-weighted anti-symmetric kernel function to the state domain and therefore propose a nonparametric procedure to test the existence of change points. When the existence of change points is affirmative, we further introduce an algorithm to estimate the number of change points together with their locations. Theoretical results of the proposed detection and estimation procedures are given and a real dataset is used to illustrate our methods., to appear in Journal of Econometrics

Distributional regression models that overcome the traditional focus on relating the conditional mean of the response to explanatory variables and instead target either the complete conditional response distribution or more general features thereof have seen increasing interest in the past decade. The current state of distributional regression will be discussed, with a particular focus on the four most prominent model classes: (i) generalized additive models for location, scale and shape, (ii) conditional transformation models and distribution regression, (iii) density regression, and (iv) quantile and expectile regression. Characteristics of the different distributional regression approaches will be provided to establish a structured overview on the similarities and differences with respect to the required assumptions on the conditional response distribution, theoretical properties, and the availability of software implementations. In addition, challenges arising in the interpretability of distributional regression models will be discussed and all four approaches will be illustrated with an application analyzing determinants of income distributions from the German Socio-Economic Panel (GSOEP).

To utilize a huge amount of observation data based on real-world events, a data assimilation process is needed to estimate the state of the system behind the observed data. The Kalman filter is a very commonly used technique in data assimilation, but it has a problem in terms of practical use from the viewpoint of processing efficiency and estimating the deterioration in precision when applied to particularly large-scale datasets. In this paper, we propose a method that simultaneously addresses these problems and demonstrate its usefulness. The proposed method improves the processing efficiency and suppresses the deterioration in estimation precision by introducing correction processes focusing on the non-negative nature and sparseness of data in wavelet space. We show that the proposed method can accurately estimate population dynamics (MAE ≤ 3, RMSE ≤ 7) on the basis of an evaluation done using population data generated from cellular networks. In addition, the possibility of wide area abnormality detection using the proposed method is shown from a situation analysis of when Category 5 typhoon Hagibis made landfall in Japan. The proposed method has been deployed in a commercial service to estimate real-time population dynamics in Japan.

The Vector AutoRegressive Moving Average (VARMA) model is fundamental to the theory of multivariate time series; however, identifiability issues have led practitioners to abandon it in favor of the simpler but more restrictive Vector AutoRegressive (VAR) model. We narrow this gap with a new optimization-based approach to VARMA identification built upon the principle of parsimony. Among all equivalent data-generating models, we use convex optimization to seek the parameterization that is "simplest" in a certain sense. A user-specified strongly convex penalty is used to measure model simplicity, and that same penalty is then used to define an estimator that can be efficiently computed. We establish consistency of our estimators in a double-asymptotic regime. Our non-asymptotic error bound analysis accommodates both model specification and parameter estimation steps, a feature that is crucial for studying large-scale VARMA algorithms. Our analysis also provides new results on penalized estimation of infinite-order VAR, and elastic net regression under a singular covariance structure of regressors, which may be of independent interest. We illustrate the advantage of our method over VAR alternatives on three real data examples.

The COVID-19 pandemic is one of the most pressing issues at present. A question which is particularly important for governments and policy makers is the following: Does the virus spread in the same way in different countries? Or are there significant differences in the development of the epidemic? In this paper, we devise new inference methods that allow to detect differences in the development of the COVID-19 epidemic across countries in a statistically rigorous way. In our empirical study, we use the methods to compare the outbreak patterns of the epidemic in a number of European countries.

Given the prevalence of depression worldwide and its major impact on society, several studies employed artificial intelligence modelling to automatically detect and assess depression. However, interpretation of these models and cues are rarely discussed in detail in the AI community, but have received increased attention lately. In this study, we aim to analyse the commonly selected features using a proposed framework of several feature selection methods and their effect on the classification results, which will provide an interpretation of the depression detection model. The developed framework aggregates and selects the most promising features for modelling depression detection from 38 feature selection algorithms of different categories. Using three real-world depression datasets, 902 behavioural cues were extracted from speech behaviour, speech prosody, eye movement and head pose. To verify the generalisability of the proposed framework, we applied the entire process to depression datasets individually and when combined. The results from the proposed framework showed that speech behaviour features (e.g. pauses) are the most distinctive features of the depression detection model. From the speech prosody modality, the strongest feature groups were F0, HNR, formants, and MFCC, while for the eye activity modality they were left-right eye movement and gaze direction, and for the head modality it was yaw head movement. Modelling depression detection using the selected features (even though there are only 9 features) outperformed using all features in all the individual and combined datasets. Our feature selection framework did not only provide an interpretation of the model, but was also able to produce a higher accuracy of depression detection with a small number of features in varied datasets. This could help to reduce the processing time needed to extract features and creating the model.

This paper estimates a panel model with endogenously time-varying parameters for COVID-19 cases and deaths in U.S. states. The functional form for infections incorporates important features of epidemiological models but is flexibly parameterized to capture different trajectories of the pandemic. Daily deaths are modeled as a spike-and-slab regression on lagged cases. The paper's Bayesian estimation reveals that social distancing and testing have significant effects on the parameters. For example, a 10 percentage point increase in the positive test rate is associated with a 2 percentage point increase in the death rate among reported cases. The model forecasts perform well, even relative to models from epidemiology and statistics.

The randomized treatment allocation process in a response adaptive clinical trial is formulated as a stochastic sequential decision problem and an algorithm is proposed to approximate the optimal value under the average reward criterion. When the information of previous treatment allocations and associated responses are summarized with sufficient statistics for unknown parameters, the decision process becomes a Markov process, on which a span-contractor operator is defined. It is proven that the average reward under the policy identified from the span-contractor operator converges almost surely to the optimal value. Numerical results reveal that the sequential procedure based on the controlled Markov process shows superior ethical advantage and at the same time produces good statistical power for large sample sizes such as 200 or larger.

Missing values in data impede the task of inference for population parameters of interest. Multiple Imputation (MI) is a popular method for handling missing data since it accounts for the uncertainty of missing values. Inference in MI involves combining point and variance estimates from each imputed dataset via Rubin’s rules. A sufficient condition for these rules is that the estimator is approximately (multivariate) normally distributed. However, these traditional combining rules get computationally cumbersome for multicomponent parameters of interest, and unreliable at high rates of missingness (due to an unstable variance matrix). New combining rules for univariate F- and Beta-statistics from multiply-imputed data are proposed for decisions about multicomponent parameters. The proposed combining rules have the advantage of being computationally convenient since they only involve univariate F- and Beta-statistics, while providing the same inferential reliability as the traditional multivariate combining rules. Simulation study is conducted to demonstrate that the proposed method has good statistical properties of maintaining low type I and type II error rates at relatively large proportions of missingness. The general applicability of the proposed method is demonstrated within a lead exposure study to assess the association between lead exposure and neurological motor function.

In this paper, we model the trajectory of the cumulative confirmed cases and deaths of COVID-19 (in log scale) via a piecewise linear trend model. The model naturally captures the phase transitions of the epidemic growth rate via change-points and further enjoys great interpretability due to its semiparametric nature. On the methodological front, we advance the nascent self-normalization (SN) technique (Shao, 2010) to testing and estimation of a single change-point in the linear trend of a nonstationary time series. We further combine the SN-based change-point test with the NOT algorithm (Baranowski et al., 2019) to achieve multiple change-point estimation. Using the proposed method, we analyze the trajectory of the cumulative COVID-19 cases and deaths for 30 major countries and discover interesting patterns with potentially relevant implications for effectiveness of the pandemic responses by different countries. Furthermore, based on the change-point detection algorithm and a flexible extrapolation function, we design a simple two-stage forecasting scheme for COVID-19 and demonstrate its promising performance in predicting cumulative deaths in the U.S.

We consider a new class of spatio-temporal models with sparse autoregressive coefficient matrices and exogenous variable. To estimate the model, we first profile the exogenous variable out of the response. This leads to a profiled model structure. Next, to overcome endogeneity issue, we propose a class of generalized methods of moment (GMM) estimators to estimate the autoregressive coefficient matrices. A novel bagging-based estimator is further developed to conquer the over-determined issue which also occurs in Chang et al. (2015) and Dou et al. (2016). An adaptive forward–backward greedy algorithm is proposed to learn the sparse structure of the autoregressive coefficient matrices. A new BIC-type selection criteria is further developed to conduct variable selection for GMM estimators. Asymptotic properties are further studied. The proposed methodology is illustrated with extensive simulation studies. A social network dataset is analyzed for illustration purpose.

For each of (i) arbitrary stochastic reset, (ii) deterministic reset with arbitrary period, (iii) reset at arbitrary constant rate, and then in the sense of either (a) first-order stochastic dominance or (b) expectation (i.e. for each of the six possible combinations of the preceding), those laws of random times are precisely characterized that are rendered no bigger [rendered no smaller; left invariant] by all possible restart laws (within the classes (i), (ii), (iii), as the case may be). Partial results in the same vein for reset with branching are obtained. In particular it is found that deterministic and arbitrary stochastic restart lead to the same characterizations, but this equivalence fails to persist for exponential (constant-rate) reset.

Objectives. To examine homicide rates in Cali, Colombia, during the 1993–2018 period, using information derived from an interagency surveillance system. Methods. We used homicide data from Cali’s Epidemiological Surveillance System to examine homicide trends by victim’s age and sex, time, and type of method used. We estimated trend changes and the annual percentage changes using joinpoint regression analyses. Results. Homicide rates per 100 000 inhabitants dropped from 102 in 1993 to 47.8 in 2018. We observed reductions in homicide rates across age and sex groups. Most homicide victims were men aged 20 to 39 years from poor, marginalized areas. Firearms were used in 84.9% of all cases. The average annual percentage change for the entire period was −3.6 (95% confidence interval = −6.7, −0.4). Conclusions. Fluctuations in homicide rates in Cali show a clear epidemic pattern, occurring concurrently with the “crack epidemic” in different countries. Reliable and timely information provided by an Epidemiological Surveillance System allowed opportune formulation of public policies to reduce the impact of violence in Cali.

A major drawback of nonlinear dimensionality reduction (DR) techniques is their inability to preserve some authentic information from the source domain, leading to projections that are often hard to interpret when it comes to observing anything other than the topological structure of the data. In this paper, we propose a nonlinear DR approach enforcing projection constraints resulting from an a priori knowledge about the structure of the data in multivariate periodical time series. We then propose several ways of exploiting this constrained projection to extract user-relevant information, such as the nominal behavior of a periodical dynamical system or the deviant behaviors which may occur at different time scales. The techniques are demonstrated on both a synthetic dataset composed of simulated multivariate data exhibiting a periodical behavior, and a real dataset corresponding to six months of sensor data acquisitions and recordings inside experimental buildings. 1 We would like to thank the Institut National de l'Energie Solaire (INES) and the CEA, LITEN, Laboratoire Energetique du Bâtiment for providing the data.

In this paper, we investigate temporal clusters of extremes defined as subsequent exceedances of high thresholds in a stationary time series. Two meaningful features of these clusters are the probability distribution of the cluster size and the ordinal patterns giving the relative positions of the data points within a cluster. Since these patterns take only the ordinal structure of consecutive data points into account, the method is robust under monotone transformations and measurement errors. We verify the existence of the corresponding limit distributions in the framework of regularly varying time series, develop non-parametric estimators and show their asymptotic normality under appropriate mixing conditions. The performance of the estimators is demonstrated in a simulated example and a real data application to discharge data of the river Rhine., Deutsche Forschungsgemeinschaft, Projekt DEAL

We estimate a structural model using data from a novel experiment investigating how investors’ preferred frequency of portfolio evaluations balance the opposing effects of ambiguity and loss aversion. Investors in the experiment face initial ambiguity concerning return distributions for an asset. They observe draws from the true return distribution of the asset, allowing them to reduce their ambiguity through time. We exploit portfolio choices and stated beliefs over possible return distributions to estimate preferences and ambiguity updating rules. We find that 70% of investors would opt for a high frequency of portfolio evaluations, reflecting the dominating effect of ambiguity aversion over loss aversion.

This paper estimates a discrete choice model of time allocation decisions made by university students. We consider investments in academic and non-academic activities, such as job placements or volunteering. Identification is achieved using data collected through a recent survey of UK university students on subjective expectations about the returns to these activities, and the enjoyment students derive from them. Unobserved heterogeneity in the choice set is addressed using a sufficient set logit method. The analysis reveals significant ethnic differences in the level of investments, expected academic and labour market returns, and enjoyment of academic and non-academic activities. Simulations suggest that existing constraints play an important role in explaining ethnic gaps in investments.

This paper investigates how migration and location choice decisions depend on a large set of location characteristics, with particular focus on measuring the importance and nature of non-monetary costs of moving. We employ a stated-preference approach to elicit respondents’ choice probabilities for a set of hypothetical choice scenarios, using two waves from the NY Fed’s Survey of Consumer Expectations. Our stated probabilistic choice approach allows us to recover the distribution of individual-level preferences for location and mobility attributes without concerns about omitted variables and selection biases that hamper analyses based on observed mobility choices alone. We estimate substantial heterogeneity in the willingness-to-pay (WTP) for location characteristics and in moving costs, both across and within demographic groups. We find moving costs to be strongly associated with attachment to the current neighborhood and dwelling and to social networks. Our results indicate evidence of sorting into current locations based on preferences for location attributes as well as a strong negative association between respondents’ non-monetary moving costs and their moving expectations and actual mobility decisions.

While a large literature is interested in the relationship between family and labor supply outcomes, little is known about the expectations of these objects at earlier stages. We examine these expectations, taking advantage of unique data from the Berea Panel Study. In addition to characterizing expectations, starting during college, the data details outcomes for ten years after graduation. Methodological contributions come from approaches to validate quality of survey expectations data and the recognition that expectations data, along with longitudinal data, can potentially help address endogeneity issues arising in the estimation of the causal effect of family on labor supply.

We analyse a long panel of households’ stock market beliefs to gain insights into the nature of the levels, dynamics, and informativeness of these expectations. In a first step, we classify respondents into one of five groups based on their beliefs data alone. In a second step, we estimate models of expectations at the group level so that belief levels, volatility, and response to information can vary freely across groups. At opposite extremes in terms of optimism we identify pessimists who expect substantially negative returns and financially sophisticated individuals whose expectations are close to the historical average. Two groups expect average returns around zero and differ only in how they respond to information: Extrapolators who become more optimistic following positive information and mean-reverters for whom the opposite is the case. The final group is characterised by its members being unable or unwilling to quantify their beliefs about future returns.

“Rational inattention” is becoming increasingly prominent in economic modeling, but there is little empirical evidence for its central premise-that the choice of attention results from a cost-benefit optimization. Observational data typically do not allow researchers to infer attention choices from observables. We fill this gap in the literature by exploiting a unique dataset of professional forecasters who update their inflation forecasts at days of their choice. In the data we observe how many forecasters update (extensive margin of updating), the magnitude of the update (intensive margin), and the objective of optimization (forecast accuracy). There are also “shifters” in incentives: A contest that increases the benefit of accurate forecasting, and the release of official data that reduces the cost of processing information. These features allow us to link observables to attention and incentive parameters. We structurally estimate a model where the decision to update and the magnitude of the update are endogenous and the latter is the outcome of a rational inattention optimization. The empirical findings provide support for the key implication of rational inattention that information-processing efforts react to changing incentives. Counterfactuals reveal that accuracy is maximized if the contest date coincides with the release of information, aligning higher benefits with lower costs of attention.

This paper considers estimation and inference about tail features when the observations beyond some threshold are censored. We first show that ignoring such tail censoring could lead to substantial bias and size distortion, even if the censored probability is tiny. Second, we propose a new maximum likelihood estimator (MLE) based on the Pareto tail approximation and derive its asymptotic properties. Third, we provide a small sample modification to the MLE by resorting to Extreme Value theory. The MLE with this modification delivers excellent small sample performance, as shown by Monte Carlo simulations. We illustrate its empirical relevance by estimating (i) the tail index and the extreme quantiles of the US individual earnings with the Current Population Survey dataset and (ii) the tail index of the distribution of macroeconomic disasters and the coefficient of risk aversion using the dataset collected by Barro and Urs{\'u}a (2008). Our new empirical findings are substantially different from the existing literature.

An approach to modelling volatile financial return series using stationary d-vine copula processes combined with Lebesgue-measure-preserving transformations known as v-transforms is proposed. By developing a method of stochastically inverting v-transforms, models are constructed that can describe both stochastic volatility in the magnitude of price movements and serial correlation in their directions. In combination with parametric marginal distributions it is shown that these models can rival and sometimes outperform well-known models in the extended GARCH family. 1

Motivated by the ABO issue of the blood bank system, in which the portions stored have constant shelf life, we consider two subsystems of perishable inventory. The two Perishable Inventory Subsystems-PIS A and PIS B, are correlated to each other through a one-way substitution of demands. Specifically, the input streams and the demand streams applied to each subsystem are four Poisson processes, which are independent of one another. However, if the shelf of PIS A (blood of type O) is empty of items, an arriving demand of type A is unsatisfied, since demand of type A cannot be satisfied by an item of type B (blood portions of type AB), but if the shelf of PIS B is empty of items, an arriving demand of type B is applied to PIS A, since demands of type B can be satisfied by both types. This one-way substitution of the issuing policy generates for PIS A a modulated Poisson demand process operating in a two-state non-Markovian environment. The performance analysis of PIS B is known from previous work. Thus, in this study we focus on the marginal performance analysis of PIS A. Based on a fluid formulation and a Markovian approximation for the one-way substitution demand process, we develop a unified approach to efficiently and accurately approximate the performance of the PIS A. The effectiveness of the approach is investigated by extensive numerical experiments.

In this article, we introduce a covariance-mean regression model with heterogeneous similarity matrices. It not only links the covariance of responses to heterogeneous similarity matrices induced by auxiliary information, but also establishes the relationship between the mean of responses and covariates. Under this new model setting, however, two statistical inference challenges are encountered. The first challenge is that the consistency of the covariance estimator based on the standard profile likelihood approach breaks down. Hence, we propose an adjustment and develop the Z -estimation and unconstrained/constrained ordinary least squares estimation methods. We demonstrate that the resulting estimators are consistent and asymptotically normal. The second challenge is testing the adequacy of the covariance-mean regression model comprising both the multivariate mean regression and the heterogeneous covariance matrices. Correspondingly, we introduce two diagnostic test statistics and then obtain their theoretical properties. The proposed estimators and tests are illustrated via extensive simulations and an empirical example study of the stock return comovement in the US stock market.

Objective Previous literature documented the traumatic consequences of exposure to disasters on psychological functioning, but little attention has been paid to the intergenerational transmission of the memory of disasters. We explored long-term effects on the memory of the Vajont dam disaster in Northeast Italy that claimed 1,910 lives in 1963. Method We collected data from 52 two-generation families in which the first generations were born before the disaster and the second generations after. The families were divided into an experimental group whose first generation survived the disaster and a control group whose first generation had moved there afterward. The interviews included an open-ended narrative on the memory of the disaster. We coded free narratives focusing on the richness of the memories (i.e., length, causes, core, aftermath), analyzing negative emotions and salience of the natural and psychological domains. Results We applied generalized linear mixed models. The richness of the memories, including references to negative emotions, diminished with lower exposure and with intergenerational transmission. Moreover, the participants built a shared representation of the disaster that did not markedly differ across exposure or generation. The reported causes were attributed more to the natural rather than the human domain; the consequences more to the psychological compared to the material domain. Conclusions Our findings highlight the processes through which collective memories of historical traumatic events are built over the long term and the way a collective identity develops to bear the burden of highly dramatic events and to transmit intergenerational lessons from the past. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Many statistical and econometric learning methods rely on Bayesian ideas, often applied or reinterpreted in a frequentist setting. Two leading examples are shrinkage estimators and model averaging estimators, such as weighted-average least squares (WALS). In many instances, the accuracy of these learning methods in repeated samples is assessed using the variance of the posterior distribution of the parameters of interest given the data. This may be permissible when the sample size is large because, under the conditions of the Bernstein--von Mises theorem, the posterior variance agrees asymptotically with the frequentist variance. In finite samples, however, things are less clear. In this paper we explore this issue by first considering the frequentist properties (bias and variance) of the posterior mean in the important case of the normal location model, which consists of a single observation on a univariate Gaussian distribution with unknown mean and known variance. Based on these results, we derive new estimators of the frequentist bias and variance of the WALS estimator in finite samples. We then study the finite-sample performance of the proposed estimators by a Monte Carlo experiment with design derived from a real data application about the effect of abortion on crime rates.

We propose a semiparametric estimator for varying coefficient models when the regressors in the nonparametric components are measured with error. Varying coefficient models are an extension of other popular semiparametric models, including partially linear and nonparametric additive models, and deliver an attractive solution to the curse-of-dimensionality. We use deconvolution kernel estimation in a two-step procedure and show that the estimator is consistent and asymptotically normally distributed. We do not assume that we know the distribution of the measurement error a priori. Instead, we suppose we have access to a repeated measurement of the noisy regressor and present results using the approach of Delaigle, Hall and Meister (2008) and, for cases when the measurement error may be asymmetric, the approach of Li and Vuong (1998) based on Kotlarski’s (1967) identity. We show that the convergence rate of the estimator is significantly reduced when the distribution of the measurement error is assumed unknown and possibly asymmetric. We study the small sample behaviour of our estimator in a simulation study and apply it to a real dataset. In particular, we consider the role of cognitive ability in augmenting the effect of risk preferences on earnings.

This paper proposes a novel nonparametric method for estimating tail jump variation measures from short-dated options, which can achieve rate-efficiency and works in a general infinite jump activity setting, avoiding parametric or semiparametric assumptions for the jump measure. The method is based on expressing the measures of interest as integrals of the Laplace transforms of the jump compensator and developing methods for recovering nonparametrically the latter from the available option data. The separation of volatility from jumps is done in a novel way by making use of the second derivative of the Laplace transform of the returns, de-biased using either the value of the Laplace transform or of its second derivative evaluated at high frequencies. A Monte Carlo study shows the superiority of the newly-developed method over existing ones in empirically realistic settings. In an empirical application to S&P 500 index options, we find risk-neutral negative market tail jump variation that is on average smaller than previous estimates of it, is generated by smaller-sized jumps, and has less dependence on the level of diffusive volatility.

Asymptotic properties of classical kernel estimators for the spectral density are studied in the locally stationary framework. In particular, it is shown that for a locally stationary process standard spectral density estimators consistently estimate the time-averaged spectral density. This result is complemented by some illustrative examples and applications including HAC-inference in the multiple linear regression model, a simple visual tool for the detection of unconditional heteroskedasticity and a test for covariance stationarity.

This paper considers the inference problems in nonlinear quantile regressions with both stationary and nonstationary covariates. The nonparametric local constant quantile estimator is proposed to estimate the unknown quantile regression function, whose asymptotic properties are established under quite general conditions. Specification testing of the quantile regression function is further considered through a statistic constructed based on the integrated squared distance between the parametric and the nonparametric estimators for the regression function. The test statistic is shown to converge to a random variable related to the local time of an Ornstein–Uhlenbeck process under the parametric null. The power of the test against local alternatives is also investigated. Additional asymptotic results on the null parametric quantile estimators and a bootstrap test are developed as well. Numerical results demonstrate that the proposed nonparametric estimator and the specification test enjoy attractive finite sample performance.

In this paper, we use Bayesian nonparametric learning to estimate the skill of actively managed mutual funds and also to estimate the population distribution of skill. A nonparametric hierarchical prior, where the hyperprior distribution is unknown and modeled with a Dirichlet Process prior, is used to model the skill parameter, with its posterior predictive distribution being an estimate of the population distribution. Our nonparametric approach is equivalent to an infinitely ordered mixture of normals where we resolve the uncertainty in the number of mixture components by learning how to partition the funds into groups according to the average ability and the variability in the skill of a group. By resolving the mixture’s uncertainty, our nonparametric prior avoids having to sequentially estimate and test an array of pre-specified, finite ordered, mixture priors. Applying our Bayesian nonparametric learning approach to a panel of actively managed, domestic equity funds, we find the population distribution of skill to be fat-tailed, skewed towards higher levels of performance, with two distinct modes – a primary mode where the average ability covers the average fees charged by funds, and a secondary mode at a performance level where a fund loses money for its investors.

Inaccurately imposing Gaussian distributional assumptions in standard multivariate time series models does not affect inference on the autoregressive coefficients but distorts both classical and Bayesian inference on the volatility matrix whenever the true error distribution has excess kurtosis relative to the multivariate normal density. Inference on the intercept is also affected whenever the innovations are generated from a non-symmetric distribution. As a result of distributional misspecification, Bayesian methods lead to asymptotically invalid posterior inference for the intercept and the volatility matrix and, consequently, invalid posterior credible sets for quantities such as impulse responses, variance decompositions and density forecasts. We propose a robust and computationally fast Bayesian procedure which delivers asymptotically correct posterior credible sets without the need for distributional assumptions. The proposed corrected Bayesian posteriors for the volatility matrix and the intercept vector are based on the asymptotic covariance of the QML estimators and admit a closed form. Implementation of the procedure requires consistent estimation of the multivariate skewness and kurtosis of the innovations, and we propose novel shrinkage estimators designed to shrink these large dimensional objects towards the skewness and kurtosis of a Gaussian vector. We extend our robust Bayesian analysis to accommodate non-Gaussian disturbances in the presence of parameter instability, by combining the estimators of the current paper with semi-parametric kernel-type methods. We demonstrate that our estimators deliver correct posterior coverage rates in an extensive Monte Carlo exercise under a variety of distributional specifications. Finally, we present empirical evidence that imposing Gaussianity or homoskedasticity assumptions on financial and uncertainty shocks is not justified and may lead to misleading empirical conclusions.

This paper considers the estimation and inference procedures for the case of a logistic panel regression model with interactive fixed effects, where multiple individual effects are allowed and the model is capable of capturing high-dimensional cross-section dependence. The proposed model also allows for heterogeneous regression coefficients. New Bayesian and non-Bayesian approaches are introduced to estimate the model parameters. We investigate the asymptotic behaviors of the estimated parameters. We show the consistency and asymptotic normality of the estimated regression coefficients and the estimated interactive fixed effects when both the cross-section and time-series dimensions of the panel go to infinity. We prove that the dimensionality of the interactive effects can be consistently estimated by the proposed information criterion. Monte Carlo simulations demonstrate the satisfactory performance of the proposed method. Finally, the method is applied to study the performance of New York City medallion drivers in terms of efficiency.

We quantise Whitney’s construction to prove the existence of a triangulation for any$$C^2$$C2manifold, so that we get an algorithm with explicit bounds. We also give a new elementary proof, which is completely geometric.

Classical game theory assumes a player's opponent is Mr. Spock—hyper-rational and capable of almost limitless logical calculation. Classical risk analysis assumes that the opponent is Nature—non-st...

In this paper, we study approximation properties of single hidden layer neural networks with weights varying on finitely many directions and thresholds from an open interval. We obtain a necessary and at the same time sufficient measure theoretic condition for density of such networks in the space of continuous functions. Further, we prove a density result for neural networks with a specifically constructed activation function and a fixed number of neurons., 12 pages

Predicting large fetuses at birth is of great interest to obstetricians. Using an NICHD Scandinavian Study that collected longitudinal ultrasound examination data during pregnancy, we estimate diagnostic accuracy parameters of estimated fetal weight (EFW) at various times during pregnancy in predicting large-for-gestational-age. We adopt a placement value based Bayesian regression model with random effects to estimate ROC curves. The use of placement values allows us to model covariate effects directly on the ROC curves and the adoption of a Bayesian approach accommodates the a priori constraint that an ROC curve of EFW near delivery should dominate another further away. The proposed methodology is shown to perform better than some alternative approaches in simulations and its application to the Scandinavian Study data suggests that diagnostic accuracy of EFW can improve about 65% from week 17 to 37 of gestation.

Although Bayesian linear mixed effects models are increasingly popular for analysis of within-subject designs in psychology and other fields, there remains considerable ambiguity on the most appropriate Bayes factor hypothesis test to quantify the degree to which the data support the presence or absence of an experimental effect. Specifically, different choices for both the null model and the alternative model are possible, and each choice constitutes a different definition of an effect resulting in a different test outcome. We outline the common approaches and focus on the impact of aggregation, the effect of measurement error, the choice of prior distribution, and the detection of interactions. For concreteness, three example scenarios showcase how seemingly innocuous choices can lead to dramatic differences in statistical evidence. We hope this work will facilitate a more explicit discussion about best practices in Bayes factor hypothesis testing in mixed models.

A stochastic calculus is given for processes described by stochastic integrals with respect to fractional Brownian motions and Rosenblatt processes somewhat analogous to the stochastic calculus for Ito processes. These processes for this stochastic calculus arise naturally from a stochastic chain rule for functionals of Rosenblatt processes; and some Ito-type expressions are given here. Furthermore, there is some analysis of these results for their applications to problems using Rosenblatt noise.

In this study, we consider cross-sectional interaction models including spatial autoregressive models and peer effects models as special cases. Our model allows the endogenous effect – the effect of others’ outcomes on one’s own outcome – to be nonlinear and nonparametric. For the model estimation, we propose a sieve instrumental variable estimator and establish both its consistency and asymptotic normality. Furthermore, we propose a nonparametric specification test for the linearity of the endogenous effect. Under the null hypothesis of linearity, we show that the test statistic is asymptotically distributed as normal. As an empirical illustration, we focus on the data on regional economic performance investigated by Gennaioli et al. (2013). This empirical analysis highlights the usefulness of the proposed model and method.

In this paper, we study the asymptotic behavior of the quadratic variation for the class of AR(1) processes driven by white noise in the second Wiener chaos. Using tools from the analysis on Wiener space, we give an upper bound for the total-variation speed of convergence to the normal law, which we apply to study the estimation of the model’s mean-reversion. Simulations are performed to illustrate the theoretical results.

We study the optimal sustainable harvesting of a population that lives in a random environment. The novelty of our setting is that we maximize the asymptotic harvesting yield, both in an expected value and almost sure sense, for a large class of harvesting strategies and unstructured population models. We prove under relatively weak assumptions that there exists a unique optimal harvesting strategy characterized by an optimal threshold below which the population is maintained at all times by utilizing a local time push-type policy. We also discuss, through Abelian limits, how our results are related to the optimal harvesting strategies when one maximizes the expected cumulative present value of the harvesting yield and establish a simple connection and ordering between the values and optimal boundaries. Finally, we explicitly characterize the optimal harvesting strategies in two different cases, one of which is the celebrated stochastic Verhulst Pearl logistic model of population growth.

We consider a Bessel process X of dimension δ ∈ ( 0 , 2 ) having 0 as a slowly reflecting (sticky) boundary point with a stickiness parameter 1 ∕ μ ∈ ( 0 , ∞ ) . We show that (i) the process X can be characterised through its square Y = X 2 as a unique weak solution to the SDE system d Y t = δ I ( Y t > 0 ) d t + 2 Y t d B t I ( Y t = 0 ) d t = 1 2 μ d l t 0 ( Y ) where B is a standard Brownian motion and l 0 ( Y ) is a diffusion local time process of Y at 0, and (ii) the transition density function of X can be expressed in the closed form as a convolution integral involving a Mittag-Leffler function and a modified Bessel function of the second kind. Appearance of the Mittag-Leffler function is novel in this context. We determine a (sticky) boundary condition at zero that characterises the transition density function of X as a unique solution to the Kolmogorov backward/forward equation of X . We also show that the convolution integral can be characterised as a unique solution to the generalised Abel equation of the second kind. Letting μ ↓ 0 (absorption) and μ ↑ ∞ (instantaneous reflection) the closed-form expression for the transition density function of X reduces to the ones found by Feller (1951) and Molchanov (1967) respectively.

High-dimensional linear regression has been intensively studied in the community of statistics in the last two decades. For the convenience of theoretical analyses, classical methods usually assume independent observations and sub-Gaussian-tailed errors. However, neither of them hold in many real high-dimensional time-series data. Recently [Sun, Zhou, Fan, 2019, J. Amer. Stat. Assoc., in press] proposed Adaptive Huber Regression (AHR) to address the issue of heavy-tailed errors. They discover that the robustification parameter of the Huber loss should adapt to the sample size, the dimensionality, and the moments of the heavy-tailed errors. We progress in a vertical direction and justify AHR on dependent observations. Specifically, we consider an important dependence structure -- Markov dependence. Our results show that the Markov dependence impacts on the adaption of the robustification parameter and the estimation of regression coefficients in the way that the sample size should be discounted by a factor depending on the spectral gap of the underlying Markov chain.

This paper adapts an actuarial mathematical model, built for the Italian public pension system, based on the law proposal 3035/2009 to the Accountant Pension Fund (CNPADC). The aim is to introduce a new philosophy pension highly correlated with the concept of adequacy for an ambitious social welfare; using the logic of the 3035/2009 proposal, which guarantees a minimum threshold for the replacement rate of the direct pension, this study provides a rigorous actuarial mathematical model that explains a sort of rate of contribution at a tendential equilibrium, in a pay-as-you-go pension system. This model reveals for which parameters it is possible to intervene to maintain the standard of living in retirement.