Fisher information and the central limit theorem

被引：29

作者：

Bobkov, Sergey G. ^{[1
]}

Chistyakov, Gennadiy P. ^{[2
]}

Goetze, Friedrich ^{[2
]}

机构：

[1] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA

[2] Univ Bielefeld, Fak Math, D-33501 Bielefeld, Germany

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2014年 / 159卷 / 1-2期

基金：

美国国家科学基金会;

关键词：

Entropy; Entropic distance; Central limit theorem; Edgeworth-type expansions; NONUNIFORM BOUNDS;

D O I：

10.1007/s00440-013-0500-5

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

070103 [概率论与数理统计]; 140311 [社会设计与社会创新];

摘要：

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.

引用

页码：1 / 59

页数：59

共 24 条

[1]

Solution of Shannon's problem on the monotonicity of entropy [J].

Artstein, S ;

Ball, KM ;

Barthe, F ;

Naor, A .

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 17 (04) :975-982

[2]

On the rate of convergence in the entropic central limit theorem [J].

Artstein, S ;

Ball, KM ;

Barthe, F ;

Naor, A .

PROBABILITY THEORY AND RELATED FIELDS, 2004, 129 (03) :381-390

[3]

Ball K, 2003, DUKE MATH J, V119, P41

[4]

Bhattacharya RN, 2010, CLASS APPL MATH, V64, P1, DOI 10.1137/1.9780898719895

[5]

Billingsley Patrick, 1999, Convergence of probability measures, V2nd

[6]

THE CONVOLUTION INEQUALITY FOR ENTROPY POWERS [J].

BLACHMAN, NM .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1965, 11 (02) :267-271

[7]

Non-Uniform Bounds in Local Limit Theorems in Case of Fractional Moments. II [J].

Bobkov, S. G. ;

Chistyakov, G. P. ;

Goetze, F. .

MATHEMATICAL METHODS OF STATISTICS, 2011, 20 (04) :269-287

[8]

Non-Uniform Bounds in Local Limit Theorems in Case of Fractional Moments. I [J].

Bobkov, S. G. ;

Chistyakov, G. P. ;

Goetze, F. .

MATHEMATICAL METHODS OF STATISTICS, 2011, 20 (03) :171-191

[9]

Bobkov S.G., ANN PROBAB IN PRESS

[10]

Large deviations and isoperimetry over convex probability measures with heavy tails [J].

Bobkov, Sergey G. .

ELECTRONIC JOURNAL OF PROBABILITY, 2007, 12 :1072-1100

← 1 2 3 →