Fisher information inequalities and the Central Limit Theorem

OT Johnson; AR Barron

doi:10.1007/s00440-004-0344-0

Fisher information inequalities and the Central Limit Theorem

OT Johnson, AR Barron

Research output: Contribution to journal › Article (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 contribution	Fisher information inequalities and the Central Limit Theorem
Original language	English
Pages (from-to)	391 - 409
Number of pages	19
Journal	Probability Theory and Related Fields
Volume	129 (3)
DOIs	https://doi.org/10.1007/s00440-004-0344-0
Publication status	Published - Jul 2004

Bibliographical note

Publisher: Springer

Access to Document

10.1007/s00440-004-0344-0

http://www.springerlink.com/content/7rb2yqmhtc134e8x/

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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.",

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AB - 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.

U2 - 10.1007/s00440-004-0344-0

DO - 10.1007/s00440-004-0344-0

M3 - Article (Academic Journal)

VL - 129 (3)

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JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

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