IMPROVED CENTRAL LIMIT THEOREM AND BOOTSTRAP APPROXIMATIONS IN HIGH DIMENSIONS

• 成果类型: Article
• 署名作者: Chernozhuokov, Victor; Chetverikov, Denis; Kato, Kengo; Koike, Yuta
• 署名单位: Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); University of California System; University of California Los Angeles; Cornell University; University of Tokyo; University of Tokyo
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/22-AOS2193
• 发表日期: 2022
• 页码: 2562-2586
• 关键词: Gaussian Approximation; inference; statistics; parameters; maxima; sums

摘要

This paper deals with the Gaussian and bootstrap approximations to the distribution of the max statistic in high dimensions. This statistic takes the form of the maximum over components of the sum of independent random vectors and its distribution plays a key role in many high-dimensional estimation and testing problems. Using a novel iterative randomized Lindeberg method, the paper derives new bounds for the distributional approximation errors. These new bounds substantially improve upon existing ones and simultaneously allow for a larger class of bootstrap methods.