Rates of Fisher information convergence in the central limit theorem for nonlinear statistics

Fuente: arXiv
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Main Author: Dung, Nguyen Tien
Format: Preprint
Published: 2022
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author Dung, Nguyen Tien
author_facet Dung, Nguyen Tien
contents We develop a general method to study the Fisher information distance in central limit theorem for nonlinear statistics. We first construct completely new representations for the score function. We then use these representations to derive quantitative estimates for the Fisher information distance. To illustrate the applicability of our approach, explicit rates of Fisher information convergence for quadratic forms and the functions of sample means are provided. For the sums of independent random variables, we obtain the Fisher information bounds without requiring the finiteness of Poincaré constant. Our method can also be used to bound the Fisher information distance in non-central limit theorems.
format Preprint
id arxiv_https___arxiv_org_abs_2205_14446
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Rates of Fisher information convergence in the central limit theorem for nonlinear statistics
Dung, Nguyen Tien
Probability
Statistics Theory
We develop a general method to study the Fisher information distance in central limit theorem for nonlinear statistics. We first construct completely new representations for the score function. We then use these representations to derive quantitative estimates for the Fisher information distance. To illustrate the applicability of our approach, explicit rates of Fisher information convergence for quadratic forms and the functions of sample means are provided. For the sums of independent random variables, we obtain the Fisher information bounds without requiring the finiteness of Poincaré constant. Our method can also be used to bound the Fisher information distance in non-central limit theorems.
title Rates of Fisher information convergence in the central limit theorem for nonlinear statistics
topic Probability
Statistics Theory
url https://arxiv.org/abs/2205.14446