Generalized entropy power inequalities and monotonicity properties of information

被引：105

作者：

Madiman, Mokshay ^{[1
]}

Barron, Andrew ^{[1
]}

机构：

[1] Yale Univ, Dept Stat, New Haven, CT 06511 USA

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2007年 / 53卷 / 07期

关键词：

central limit theorem; entropy power; information inequalities;

D O I：

10.1109/TIT.2007.899484

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

New families of Fisher information and entropy power inequalities for sums of independent random variables are presented. These inequalities relate the information in the sum of n independent random variables to the information contained in sums over subsets of the random variables, for an arbitrary collection of subsets. As a consequence, a simple proof of the monotonicity of information in central limit theorems is obtained, both in the setting of independent and identically distributed (i.i.d.) summands as well as in the more general setting of independent summands with variance-standardized sums.

引用

页码：2317 / 2329

页数：13

共 45 条

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