Improved central limit theorem and bootstrap approximations in high dimensions
By Victor Chernozhukov, D. Chetverikov, Kengo Kato, Yuta Koike. Annals of Statistics, 2019
95 citations recorded by the source corpus.
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.
Subfields: Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/80fd93f7d7ff5d99c00b63c00d5c2fa099c34e75
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In Statistics and Probability
- Victor Chernozhukov
- D. Chetverikov
- Yuta Koike
- Kengo Kato
- Alexandre Belloni
- Christian Hansen
- Whitney K. Newey
- Stefan Wager
Citations in the corpus
- High-dimensional central limit theorems by Stein’s method (2020, unknown): “…random vectors, many articles have been devoted to the development of this subject: For example, see Chernozhukov, Chetverikov and Kato (2017a), Chernozhukov et al. (2019) for generalization to normal approximation on hyperrectangles and improvements of the error bound, Chen (2018), Chen and…”
- Nearly optimal central limit theorem and bootstrap approximations in high dimensions (2020, methodology): “..,n; and also consider condition (M) n−1 Pn i=1 IE|Xij/σj| 4 ≤ B2 nfor all j= 1,...,p; 8 CHERNOZHUKOV, CHETVERIKOV, AND KOIKE Similar conditions were previously used and motivated by applications in [12, 15, 17, 20, 23, 19]. Corollary 2.1 (Gaussian Approximation under Simple Conditions). Under cond”