October 2022 Improved central limit theorem and bootstrap approximations in high dimensions
Victor Chernozhuokov, Denis Chetverikov, Kengo Kato, Yuta Koike
Author Affiliations +
Ann. Statist. 50(5): 2562-2586 (October 2022). DOI: 10.1214/22-AOS2193


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.

Funding Statement

K. Kato is suport by the NSF Grant DMS-1952306 and DMS-2014636.


We are grateful to Tim Armstrong, Matias Cattaneo, Xiaohong Chen and Tengyuan Liang for helpful discussions. We also thank seminar participants at the University of Pennsylvania and Yale University.


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Victor Chernozhuokov. Denis Chetverikov. Kengo Kato. Yuta Koike. "Improved central limit theorem and bootstrap approximations in high dimensions." Ann. Statist. 50 (5) 2562 - 2586, October 2022. https://doi.org/10.1214/22-AOS2193


Received: 1 June 2020; Revised: 1 January 2022; Published: October 2022
First available in Project Euclid: 27 October 2022

MathSciNet: MR4500619
zbMATH: 07628832
Digital Object Identifier: 10.1214/22-AOS2193

Primary: 60F05 , 62E17

Keywords: bootstrap , central limit theorem , iterative randomized Lindeberg method , Stein kernel

Rights: Copyright © 2022 Institute of Mathematical Statistics


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Vol.50 • No. 5 • October 2022
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