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 econometric
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.
Description
[1912.10529] Improved Central Limit Theorem and bootstrap approximations in high dimensions
%0 Journal Article
%1 chernozhukov2019improved
%A Chernozhukov, Victor
%A Chetverikov, Denis
%A Kato, Kengo
%A Koike, Yuta
%D 2019
%K approximate bayesian probability readings stats theory
%T Improved Central Limit Theorem and bootstrap approximations in high
dimensions
%U http://arxiv.org/abs/1912.10529
%X 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 econometric
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.
@article{chernozhukov2019improved,
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 econometric
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.},
added-at = {2019-12-25T16:25:38.000+0100},
author = {Chernozhukov, Victor and Chetverikov, Denis and Kato, Kengo and Koike, Yuta},
biburl = {https://www.bibsonomy.org/bibtex/24afa6e17109839a929641d4c184586dd/kirk86},
description = {[1912.10529] Improved Central Limit Theorem and bootstrap approximations in high dimensions},
interhash = {cb43ef3ea9635b5edac1e8cf8fe53860},
intrahash = {4afa6e17109839a929641d4c184586dd},
keywords = {approximate bayesian probability readings stats theory},
note = {cite arxiv:1912.10529Comment: 53 pages},
timestamp = {2019-12-25T16:25:38.000+0100},
title = {Improved Central Limit Theorem and bootstrap approximations in high
dimensions},
url = {http://arxiv.org/abs/1912.10529},
year = 2019
}