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

Mathematics

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

14 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

Access

10.1214/18-AOP1261

OpenUrl availability

Full text

Cite this

@article{5bf7afa2865f4ab0b223f8f259dc16da,

title = "R{\'e}nyi divergence and the central limit theorem",

abstract = " We explore properties of the χ 2 and R{\'e}nyi 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).",

keywords = "Central limit theorem, R{\'e}nyi and Tsallis entropies, χ -divergence",

author = "Bobkov, {S. G.} and Chistyakov, {G. P.} and F. G{\"o}tze",

note = "Publisher Copyright: {\textcopyright} Institute of Mathematical Statistics, 2019.",

year = "2019",

month = jan,

day = "1",

doi = "10.1214/18-AOP1261",

language = "English (US)",

volume = "47",

pages = "270--323",

journal = "Annals of Probability",

issn = "0091-1798",

publisher = "Institute of Mathematical Statistics",

number = "1",

}

TY - JOUR

T1 - Rényi divergence and the central limit theorem

AU - Bobkov, S. G.

AU - Chistyakov, G. P.

AU - Götze, F.

N1 - Publisher Copyright: © Institute of Mathematical Statistics, 2019.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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).

AB - 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).

KW - Central limit theorem

KW - Rényi and Tsallis entropies

KW - χ -divergence

UR - http://www.scopus.com/inward/record.url?scp=85061778113&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85061778113&partnerID=8YFLogxK

U2 - 10.1214/18-AOP1261

DO - 10.1214/18-AOP1261

M3 - Article

AN - SCOPUS:85061778113

SN - 0091-1798

VL - 47

SP - 270

EP - 323

JO - Annals of Probability

JF - Annals of Probability

IS - 1

ER -

Rényi divergence and the central limit theorem

Abstract

Bibliographical note

Keywords

Access

OpenUrl availability

Other files and links

Fingerprint

Cite this