High-dimensional Data Bootstrap

TL;DR

This paper reviews recent advances in high-dimensional bootstrap methods, focusing on theoretical results, applications in inference, and future research directions in high-dimensional statistics.

Contribution

It provides a comprehensive overview of high-dimensional bootstrap theory, applications, and future challenges, synthesizing recent progress in the field.

Findings

Summarizes high-dimensional CLTs and bootstrap consistency results.

Reviews applications in confidence sets, hypothesis testing, and policy inference.

Discusses future research directions in high-dimensional bootstrap.

Abstract

This article reviews recent progress in high-dimensional bootstrap. We first review high-dimensional central limit theorems for distributions of sample mean vectors over the rectangles, bootstrap consistency results in high dimensions, and key techniques used to establish those results. We then review selected applications of high-dimensional bootstrap: construction of simultaneous confidence sets for high-dimensional vector parameters, multiple hypothesis testing via stepdown, post-selection inference, intersection bounds for partially identified parameters, and inference on best policies in policy evaluation. Finally, we also comment on a couple of future research directions.