Rate of convergence and edgeworth-type expansion in the entropic central limit theorem

Sergey G. Bobkov; Gennadiy P. Chistyakov; Friedrich Götze

doi:10.1214/12-AOP780

Rate of convergence and edgeworth-type expansion in the entropic central limit theorem

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

School of Mathematics

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

27 Scopus citations

Abstract

An Edgeworth-type expansion is established for the entropy distance to the class of normal distributions of sums of i.i.d. random variables or vectors, satisfying minimal moment conditions.

Original language	English (US)
Pages (from-to)	2479-2512
Number of pages	34
Journal	Annals of Probability
Volume	41
Issue number	4
DOIs	https://doi.org/10.1214/12-AOP780
State	Published - 2013

Keywords

Central limit theorem
Edgeworth-type expansions
Entropic distance
Entropy

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title = "Rate of convergence and edgeworth-type expansion in the entropic central limit theorem",

abstract = "An Edgeworth-type expansion is established for the entropy distance to the class of normal distributions of sums of i.i.d. random variables or vectors, satisfying minimal moment conditions.",

keywords = "Central limit theorem, Edgeworth-type expansions, Entropic distance, Entropy",

author = "Bobkov, {Sergey G.} and Chistyakov, {Gennadiy P.} and Friedrich G{\"o}tze",

year = "2013",

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AU - Bobkov, Sergey G.

AU - Chistyakov, Gennadiy P.

AU - Götze, Friedrich

PY - 2013

Y1 - 2013

N2 - An Edgeworth-type expansion is established for the entropy distance to the class of normal distributions of sums of i.i.d. random variables or vectors, satisfying minimal moment conditions.

AB - An Edgeworth-type expansion is established for the entropy distance to the class of normal distributions of sums of i.i.d. random variables or vectors, satisfying minimal moment conditions.

KW - Central limit theorem

KW - Edgeworth-type expansions

KW - Entropic distance

KW - Entropy

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JO - Annals of Probability

JF - Annals of Probability

IS - 4

ER -

Rate of convergence and edgeworth-type expansion in the entropic central limit theorem

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