## 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 |
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Original language | English |

Pages (from-to) | 391 - 409 |

Number of pages | 19 |

Journal | Probability Theory and Related Fields |

Volume | 129 (3) |

DOIs | |

Publication status | Published - Jul 2004 |