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

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