Entropy inequalities and the Central Limit Theorem

被引：15

作者：

Johnson, O ^{[1
]}

机构：

[1] Univ Cambridge, Stat Lab, Cambridge CB2 1SB, England

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2000年 / 88卷 / 02期

基金：

英国工程与自然科学研究理事会;

关键词：

normal convergence; entropy; Fisher information;

D O I：

10.1016/S0304-4149(00)00006-5

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Motivated by Barren (1986, Ann. Probab. 14, 336-342), Brown (1982, Statistics and Probability: Essays in Honour of C.R. Rao, pp. 141-148) and Carlen and Soffer (1991, Comm. Math. Phys. 140, 339-371), we prove a version of the Lindeberg-Feller Theorem, showing normal convergence of the normalised sum of independent, not necessarily identically distributed random variables, under standard conditions. We give a sufficient condition for convergence in the relative entropy sense of Kullback-Leibler, which is strictly stronger than L-1. In the IID case we recover the main result of Barren [1] (c) 2000 Elsevier Science B.V. All rights reserved.

引用

页码：291 / 304

页数：14

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