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This paper investigates the idea of designing data-driven partial estimators for nonlinear systems showing parametric uncertainties using sparse multivariate polynomial relationships. A general framework is first presented and then…
We consider partially-specified optimization problems where the goal is to actively, but efficiently, acquire missing information about the problem in order to solve it. An algorithm designer wishes to solve a linear program (LP), $\max…
The paper considers linear regression problems where the number of predictor variables is possibly larger than the sample size. The basic motivation of the study is to combine the points of view of model selection and functional regression…
Numerous studies have been devoted to the estimation and inference problems for functional linear models (FLM). However, few works focus on model checking problem that ensures the reliability of results. Limited tests in this area do not…
We introduce a generic class of dynamic nonlinear heterogeneous parameter models that incorporate individual and time fixed effects in both the intercept and slope. These models are subject to the incidental parameter problem, in that the…
Nonparametric regression is a standard statistical tool with increased importance in the Big Data era. Boundary points pose additional difficulties but local polynomial regression can be used to alleviate them. Local linear regression, for…
Hierarchical Bayesian models are increasingly used in large, inhomogeneous complex network dynamical systems by modeling parameters as draws from a hyperparameter-governed distribution. However, theoretical guarantees for these estimates as…
We propose nonparametric methods for functional linear regression which are designed for sparse longitudinal data, where both the predictor and response are functions of a covariate such as time. Predictor and response processes have smooth…
Empirical growth analysis has three major problems --- variable selection, parameter heterogeneity and cross-sectional dependence --- which are addressed independently from each other in most studies. The purpose of this study is to propose…
This paper addresses classification problems with matrix-valued data, which commonly arise in applications such as neuroimaging and signal processing. Building on the assumption that the data from each class follows a matrix normal…
This paper aims to develop an optimality theory for linear discriminant analysis in the high-dimensional setting. A data-driven and tuning free classification rule, which is based on an adaptive constrained $\ell_1$ minimization approach,…
We study partially linear models when the outcome of interest and some of the covariates are observed in two different datasets that cannot be linked. This type of data combination problem arises very frequently in empirical microeconomics.…
In this paper, we consider the situation in which the observations follow an isotonic generalized partly linear model. Under this model, the mean of the responses is modelled, through a link function, linearly on some covariates and…
A new empirical Bayes approach to variable selection in the context of generalized linear models is developed. The proposed algorithm scales to situations in which the number of putative explanatory variables is very large, possibly much…
Many statistical estimands can expressed as continuous linear functionals of a conditional expectation function. This includes the average treatment effect under unconfoundedness and generalizations for continuous-valued and personalized…
We consider the problem of multi-task learning in the high dimensional setting. In particular, we introduce an estimator and investigate its statistical and computational properties for the problem of multiple connected linear regressions…
Anomaly detection in large populations is a challenging but highly relevant problem. The problem is essentially a multi-hypothesis problem, with a hypothesis for every division of the systems into normal and anomal systems. The number of…
Estimating heterogeneous treatment effects is an important problem across many domains. In order to accurately estimate such treatment effects, one typically relies on data from observational studies or randomized experiments. Currently,…
Missing data is a common problem in clinical data collection, which causes difficulty in the statistical analysis of such data. In this article, we consider the problem under a framework of a semiparametric partially linear model when…
This paper introduces the method of composite quantile factor model for factor analysis in high-dimensional panel data. We propose to estimate the factors and factor loadings across multiple quantiles of the data, allowing the estimates to…