Fisher information inequalities and the Central Limit Theorem

OT Johnson, AR Barron

Research output: Contribution to journalArticle (Academic Journal)peer-review

86 Citations (Scopus)

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 Poincar\'{e} 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.
Translated title of the contributionFisher information inequalities and the Central Limit Theorem
Original languageEnglish
Pages (from-to)391 - 409
Number of pages19
JournalProbability Theory and Related Fields
Volume129 (3)
DOIs
Publication statusPublished - Jul 2004

Bibliographical note

Publisher: Springer

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