Rényi divergence and the central limit theorem

S. G. Bobkov; G. P. Chistyakov; F. Götze

doi:10.1214/18-AOP1261

Rényi divergence and the central limit theorem

S. G. Bobkov, G. P. Chistyakov, F. Götze

School of Mathematics

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

We explore properties of the χ ² and Rényi distances to the normal law and in particular propose necessary and sufficient conditions under which these distances tend to zero in the central limit theorem (with exact rates with respect to the increasing number of summands).

Original language	English (US)
Pages (from-to)	270-323
Number of pages	54
Journal	Annals of Probability
Volume	47
Issue number	1
DOIs	https://doi.org/10.1214/18-AOP1261
State	Published - Jan 1 2019

Bibliographical note

Publisher Copyright:
© Institute of Mathematical Statistics, 2019.

Keywords

Central limit theorem
Rényi and Tsallis entropies
χ -divergence

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10.1214/18-AOP1261

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Rényi divergence and the central limit theorem

Abstract

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Keywords

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