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Improved Central Limit Theorem and bootstrap approximations in high dimensions

Victor Chernozhukov, Denis Chetverikov, Kengo Kato, Yuta Koike

arXiv 22 Dec 2019 · Mathematics — Statistics Theory · publishedThe Annals of Statistics (2022) · 53 citations (OpenAlex)

arXiv:1912.10529 · PDF · DOI · OpenAlex · Extracted main text

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.

Citation extraction

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Koike, Y (2021) Notes on the dimension dependence in high-dimensional central limit theorems for hyperrectangles self1.00063100%
2Deng, H. and Zhang, C.-H (2020) Beyond Gaussian approximation: bootstrap for maxima of sums of independent random vectors0.95014486%
3Chernozhukov, V., Chetverikov, D. and Kato, K (2017) Central limit theorems and bootstrap in high dimensions self0.88810670%
4Chernozhukov, V., Chetverikov, D. and Kato, K (2013) Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors self0.8307557%
5O'Donnell, R., Servedio, R., and Tan, L (2019) Fooling polytopes0.7374350%
6Belloni, A., Chernozhukov, V., Chetverikov, D., Hansen, C., and Kato… (2018) High-dimensional econometrics and regularized GMM self0.73732100%
7van der Vaart, A.W. and Wellner, J.A (1996) Weak Convergence and Empirical Processes: With Applications to Statistics0.6443267%
8Koike, Y (2019) High-dimensional central limit theorems for homogeneous sums self0.64422100%
9Mammen, E (1993) Bootstrap and wild bootstrap for high dimensional linear models0.64422100%
10Chernozhukov, V., Chetverikov, D. and Kato, K (2015) Comparison and anti-concentration bounds for maxima of Gaussian random vectors self0.5506417%

Showing the top 10 of 43 scored citations.

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