Fisher Information inequalities and the Central Limit Theorem

Details Fisher Information inequalities and the Central Limit Theorem Fisher Information inequalities and the Central Limit Theorem

2001-11-02

arxiv.org/abs/math/0111020v2

Probability Theory and Related Fields, Vol 129/3, 2004, pages 391-409

Mathematics

Statistics Theory

19 pages

Scientific paper

10.1007/s00440-004-0344-0

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 L2 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.

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