Statistical Inference and Large-scale Multiple Testing for High-dimensional Regression Models

This paper presents a selective survey of recent developments in statistical inference and multiple testing for high-dimensional regression models, including linear and logistic regression. We examine the construction of confidence intervals and hypothesis tests for various low-dimensional objectives such as regression coefficients and linear and quadratic functionals. The key technique is to generate debiased and desparsified estimators for the targeted low-dimensional objectives and estimate their uncertainty. In addition to covering the motivations for and intuitions behind these statistical methods, we also discuss their optimality and adaptivity in the context of high-dimensional inference. In addition, we review the recent development of statistical inference based on multiple regression models and the advancement of large-scale multiple testing for high-dimensional regression. The R package SIHR has implemented some of the high-dimensional inference methods discussed in this paper.