RATE OF CONVERGENCE AND EXPANSION OF RNYI ENTROPIC CENTRAL LIMIT THEOREM

被引：2

作者：

孙建强 ^{[1
,2
]}

丁义明 ^{[1
,3
]}

机构：

[1] Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences

[2] University of Chinese Academy of Sciences

[3] National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences

来源：

Acta Mathematica Scientia | 2015年 / 01期

关键词：

Rényi divergence; central limit theorem; Edgeworth-type expansion; rate of convergence;

D O I：

暂无

中图分类号：

O211.4 [极限理论];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We obtain the expansion of Rényi divergence of order α(0 < α < 1) between the normalized sum of IID continuous random variables and the Gaussian limit under minimal moment conditions via Edgeworth-type expansion. The rate is faster than that of Shannon case, which can be used to improve the rate of convergence in total variance norm.

引用

页码：79 / 88

页数：10

共 50 条

[1] RATE OF CONVERGENCE AND EXPANSION OF RENYI ENTROPIC CENTRAL LIMIT THEOREM
Sun, Jianqiang
Ding, Yiming
ACTA MATHEMATICA SCIENTIA, 2015, 35 (01) : 79 - 88
[2] On the rate of convergence in the entropic central limit theorem
Artstein, S
Ball, KM
Barthe, F
Naor, A
PROBABILITY THEORY AND RELATED FIELDS, 2004, 129 (03) : 381 - 390
[3] On the rate of convergence in the entropic central limit theorem
Shiri Artstein
Keith M. Ball
Franck Barthe
Assaf Naor
Probability Theory and Related Fields, 2004, 129 : 381 - 390
[4] RATE OF CONVERGENCE AND EDGEWORTH-TYPE EXPANSION IN THE ENTROPIC CENTRAL LIMIT THEOREM
Bobkov, Sergey G.
Chistyakov, Gennadiy P.
Goetze, Friedrich
ANNALS OF PROBABILITY, 2013, 41 (04) : 2479 - 2512
[5] Notes on the speed of entropic convergence in the central limit theorem
Miclo, L
STOCHASTIC INEQUALITIES AND APPLICATIONS, 2003, 56 : 129 - 156
[6] On the rate of convergence in the martingale central limit theorem
Mourrat, Jean-Christophe
BERNOULLI, 2013, 19 (02) : 633 - 645
[7] Central limit theorem with rate of convergence under sublinear
Zhou, Qianqian
Sakhanenko, Alexander
Guo, Junyi
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2024, 172
[8] On the rate of convergence in the central limit theorem for martingale difference sequences
Ouchti, L
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2005, 41 (01): : 35 - 43
[9] ON NONUNIFORM CONVERGENCE RATE ESTIMATES IN THE CENTRAL LIMIT THEOREM
Nefedova, Yu. S.
Shevtsova, I. G.
THEORY OF PROBABILITY AND ITS APPLICATIONS, 2013, 57 (01) : 28 - 59
[10] An Improved Central Limit Theorem and Fast Convergence Rates for Entropic Transportation Costs
del Barrio, Eustasio
Sanz, Alberto Gonzalez
Loubes, Jean-Michel
Niles-Weed, Jonathan
SIAM JOURNAL ON MATHEMATICS OF DATA SCIENCE, 2023, 5 (03): : 639 - 669

← 1 2 3 4 5 →