Stability of Cramer’s Characterization of Normal Laws in Information Distances

Sergey Bobkov; Gennadiy Chistyakov; Friedrich Götze

doi:10.1007/978-3-319-40519-3_1

Stability of Cramer’s Characterization of Normal Laws in Information Distances

Sergey Bobkov, Gennadiy Chistyakov, Friedrich Götze

School of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

Optimal stability estimates in the class of regularized distributions are derived for the characterization of normal laws in Cramer’s theorem with respect to relative entropy and Fisher information distance.

Original language	English (US)
Title of host publication	Progress in Probability
Publisher	Birkhauser
Pages	3-35
Number of pages	33
DOIs	https://doi.org/10.1007/978-3-319-40519-3_1
State	Published - 2016

Publication series

Name	Progress in Probability
Volume	71
ISSN (Print)	1050-6977
ISSN (Electronic)	2297-0428

Bibliographical note

Funding Information:
The authors are grateful to the referee for careful reading of the paper and valuable remarks. Bobkov?s research was partially supported by SFB 701 at Bielefeld University, Humboldt Foundation and NSF grant DMS-1612961. Chystyakov and G?tze?s research was partially supported by SFB 701.

Publisher Copyright:
© 2016, Springer International Publishing Switzerland.

Keywords

Characterization of normal laws
Cramer’s theorem
Stability problems

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10.1007/978-3-319-40519-3_1

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title = "Stability of Cramer{\textquoteright}s Characterization of Normal Laws in Information Distances",

abstract = "Optimal stability estimates in the class of regularized distributions are derived for the characterization of normal laws in Cramer{\textquoteright}s theorem with respect to relative entropy and Fisher information distance.",

keywords = "Characterization of normal laws, Cramer{\textquoteright}s theorem, Stability problems",

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

note = "Funding Information: The authors are grateful to the referee for careful reading of the paper and valuable remarks. Bobkov?s research was partially supported by SFB 701 at Bielefeld University, Humboldt Foundation and NSF grant DMS-1612961. Chystyakov and G?tze?s research was partially supported by SFB 701. Publisher Copyright: {\textcopyright} 2016, Springer International Publishing Switzerland.",

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doi = "10.1007/978-3-319-40519-3_1",

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series = "Progress in Probability",

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TY - CHAP

T1 - Stability of Cramer’s Characterization of Normal Laws in Information Distances

AU - Bobkov, Sergey

AU - Chistyakov, Gennadiy

AU - Götze, Friedrich

N1 - Funding Information: The authors are grateful to the referee for careful reading of the paper and valuable remarks. Bobkov?s research was partially supported by SFB 701 at Bielefeld University, Humboldt Foundation and NSF grant DMS-1612961. Chystyakov and G?tze?s research was partially supported by SFB 701. Publisher Copyright: © 2016, Springer International Publishing Switzerland.

PY - 2016

Y1 - 2016

N2 - Optimal stability estimates in the class of regularized distributions are derived for the characterization of normal laws in Cramer’s theorem with respect to relative entropy and Fisher information distance.

AB - Optimal stability estimates in the class of regularized distributions are derived for the characterization of normal laws in Cramer’s theorem with respect to relative entropy and Fisher information distance.

KW - Characterization of normal laws

KW - Cramer’s theorem

KW - Stability problems

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U2 - 10.1007/978-3-319-40519-3_1

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M3 - Chapter

AN - SCOPUS:85118424343

T3 - Progress in Probability

SP - 3

EP - 35

BT - Progress in Probability

PB - Birkhauser

ER -

Stability of Cramer’s Characterization of Normal Laws in Information Distances

Abstract

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Bibliographical note

Keywords

Publisher link

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