RATE OF CONVERGENCE AND EXPANSION OF RÉNYI ENTROPIC CENTRAL LIMIT THEOREM

doi:10.1016/S0252-9602(14)60140-5

数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (1): 79-88.doi: 10.1016/S0252-9602(14)60140-5

RATE OF CONVERGENCE AND EXPANSION OF RÉNYI ENTROPIC CENTRAL LIMIT THEOREM

孙建强|丁义明^*

Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences and University ofChinese Academy of Sciences, Wuhan 430071, China Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences, Beijing 100190, China

收稿日期:2014-02-27 修回日期:2014-10-13 出版日期:2015-01-20 发布日期:2015-01-20
通讯作者: 丁义明,ding@wipm.ac.cn E-mail:sunjianqiang09@mails.ucas.ac.cn;
基金资助:
This work is supported by National Basic Research Program of China (973 Program) (2011CB707802, 2013CB910200) and Natural Science Foundation of China Grant (11126180).

RATE OF CONVERGENCE AND EXPANSION OF RÉNYI ENTROPIC CENTRAL LIMIT THEOREM

SUN Jian Qiang, DING Yi Ming*

Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences and University ofChinese Academy of Sciences, Wuhan 430071, China Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences, Beijing 100190, China

Received:2014-02-27 Revised:2014-10-13 Online:2015-01-20 Published:2015-01-20
Contact: DING Yi Ming,ding@wipm.ac.cn E-mail:sunjianqiang09@mails.ucas.ac.cn;
Supported by:
This work is supported by National Basic Research Program of China (973 Program) (2011CB707802, 2013CB910200) and Natural Science Foundation of China Grant (11126180).

摘要/Abstract

摘要：

We obtain the expansion of R´enyi 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.

关键词: Rényi divergence, central limit theorem, Edgeworth-type expansion, rate of convergence

Abstract:

Key words: Rényi divergence, central limit theorem, Edgeworth-type expansion, rate of convergence

中图分类号:

62B10

孙建强|丁义明. RATE OF CONVERGENCE AND EXPANSION OF RÉNYI ENTROPIC CENTRAL LIMIT THEOREM[J]. 数学物理学报(英文版), 2015, 35(1): 79-88.

SUN Jian Qiang, DING Yi Ming. RATE OF CONVERGENCE AND EXPANSION OF RÉNYI ENTROPIC CENTRAL LIMIT THEOREM[J]. Acta mathematica scientia,Series B, 2015, 35(1): 79-88.

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RATE OF CONVERGENCE AND EXPANSION OF RÉNYI ENTROPIC CENTRAL LIMIT THEOREM

RATE OF CONVERGENCE AND EXPANSION OF RÉNYI ENTROPIC CENTRAL LIMIT THEOREM

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