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Fisher information inequalities and the central limit theorem

Fisher information inequalities and the central limit theorem 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 Poincaré 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Probability Theory and Related Fields Springer Journals

Fisher information inequalities and the central limit theorem

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References (23)

Publisher
Springer Journals
Copyright
Copyright © 2004 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics
ISSN
0178-8051
eISSN
1432-2064
DOI
10.1007/s00440-004-0344-0
Publisher site
See Article on Publisher Site

Abstract

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 Poincaré 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.

Journal

Probability Theory and Related FieldsSpringer Journals

Published: Apr 29, 2004

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