Improved central limit theorem and bootstrap approximations in high dimensions
Victor Chernozhuokov, Denis Chetverikov, Kengo Kato, Yuta Koike
The Annals of Statistics · 2022 · Volume 50 · Issue 5
Abstract
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.
Keywords
60F05, 62E17, bootstrap, central limit theorem, iterative randomized Lindeberg method, Stein kernel
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