Berry–Esseen bounds in the entropic central limit theorem

By Sergey G. Bobkov, Gennadiy P. Chistyakov, Friedrich Götze. 2011

72 citations recorded by the source corpus.

Berry–Esseen-type bounds for total variation and relative entropy distances to the normal law are established for the sums of non-i.i.d. random variables.

Subfields: Artificial Intelligence, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/59e0adbeea3f47d0f650eff3e493324f9447b7db

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Citations in the corpus

A high-dimensional CLT in W2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {W}_2$$\end{document} distance wi (2017, background): “An alternative proof of Rio’s result for W 2 was given by Bobkov [7] (see also [8]).”
Stein’s method, logarithmic Sobolev and transport inequalities (2014, background): “ actually provide a complete picture with rate O(1 n ) under a fourth-moment condition on X based on local central limit theorems and Edgeworth expansions. General sums T = Pn k=1 akXk are studied in [B-C-G3] as a particular case of sums of independent non-identically distributed random variables. V”
On Kac's chaos and related problems (2012, methodology): “ocal CLT have been established 42 M. HAURAY AND S. MISCHLER corresponding to diﬀerent regularity assumption made on the probability measure g, we refer the interested reader to the recent works [63], [8], [3] and the references therein. The proof of Theorem 4.6 use the following technical lemma whic”