Fisher information inequalities and the central limit theorem

被引：99

作者：

Johnson, O

Barron, A

机构：

[1] Statslab, Cambridge CB3 0WB, England

[2] Yale Univ, Dept Stat, New Haven, CT 06520 USA

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2004年 / 129卷 / 03期

关键词：

normal convergence; entropy; Fisher information; Poincare inequalities; rates of convergence;

D O I：

10.1007/s00440-004-0344-0

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 [统计学]; 070103 [概率论与数理统计]; 0714 [统计学];

摘要：

We give conditions for an O(1/n) rate of convergence of Fisher information and relative entropy in the Central Limit Theorem. We use the theory of projections in L-2 spaces and Poincare inequalities, to provide a better understanding of the decrease in Fisher information implied by results of Barron and Brown. We show that if the standardized Fisher information ever becomes finite then it converges to zero.

引用

页码：391 / 409

页数：19

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