Fisher information and the central limit theorem

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

doi:10.1007/s00440-013-0500-5

Fisher information and the central limit theorem

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

Mathematics

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

18 Scopus citations

Abstract

An Edgeworth-type expansion is established for the relative Fisher information distance to the class of normal distributions of sums of i.i.d. random variables, satisfying moment conditions. The validity of the central limit theorem is studied via properties of the Fisher information along convolutions.

Original language	English (US)
Pages (from-to)	1-59
Number of pages	59
Journal	Probability Theory and Related Fields
Volume	159
Issue number	1-2
DOIs	https://doi.org/10.1007/s00440-013-0500-5
State	Published - Jun 2014

Keywords

Central limit theorem
Edgeworth-type expansions
Entropic distance
Entropy

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title = "Fisher information and the central limit theorem",

abstract = "An Edgeworth-type expansion is established for the relative Fisher information distance to the class of normal distributions of sums of i.i.d. random variables, satisfying moment conditions. The validity of the central limit theorem is studied via properties of the Fisher information along convolutions.",

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

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

year = "2014",

month = jun,

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language = "English (US)",

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journal = "Probability Theory and Related Fields",

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T1 - Fisher information and the central limit theorem

AU - Bobkov, Sergey G.

AU - Chistyakov, Gennadiy P.

AU - Götze, Friedrich

PY - 2014/6

Y1 - 2014/6

N2 - An Edgeworth-type expansion is established for the relative Fisher information distance to the class of normal distributions of sums of i.i.d. random variables, satisfying moment conditions. The validity of the central limit theorem is studied via properties of the Fisher information along convolutions.

AB - An Edgeworth-type expansion is established for the relative Fisher information distance to the class of normal distributions of sums of i.i.d. random variables, satisfying moment conditions. The validity of the central limit theorem is studied via properties of the Fisher information along convolutions.

KW - Central limit theorem

KW - Edgeworth-type expansions

KW - Entropic distance

KW - Entropy

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EP - 59

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

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ER -

Fisher information and the central limit theorem

Abstract

Keywords

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