High-dimensional Data Bootstrap

2022/05/19 by Victor Chernozhukov, Chernozhukov, Victor, Denis Chetverikov +5 · 4 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Econometrics (econ.EM) #FOS: Economics and business #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2205.09691

openalex publication_date 2022/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Accuracy of Uniform Inference on Fine Grid Points
• Unifiedly Efficient Inference on All-Dimensional Targets for Large-Scale GLMs
• Making Interpretable Discoveries from Unstructured Data: A High-Dimensional Multiple Hypothesis Testing Approach
• A General Test for Independent and Identically Distributed Hypothesis

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