English

Fisher Information inequalities and the Central Limit Theorem

Statistics Theory 2007-06-13 v2 Probability Statistics Theory

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 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.

Cite

@article{arxiv.math/0111020,
  title  = {Fisher Information inequalities and the Central Limit Theorem},
  author = {Oliver Johnson and Andrew Barron},
  journal= {arXiv preprint arXiv:math/0111020},
  year   = {2007}
}

Comments

19 pages

R2 v1 2026-07-22T16:41:21.097Z