Entropy inequalities and the central limit theorem.
type: Item
instance of: scholarly article
title: Entropy inequalities and the central limit theorem.
zbMATH Open document ID: 1045.60023
DOI: 10.1016/S0304-4149(00)00006-5
author: Oliver Johnson
published in: Stochastic Processes and their Applications
publication date: 2004-09-07T00:00:00Z
review text: The paper presents two versions of central limit theorems for normalized partial sums of independent real-valued random variables, not necessarily identically distributed. The variables are assumed possessing densities (with respect to Lebesgue measure) and fulfilling some standard conditions as a uniform Lindeberg condition, bounded variance condition, etc. Theorem 1 shows convergence in Fischer information implying weak convergence and Theorem 2 shows convergence in Kullback-Leibler distance inducing \(L_1\)-convergence.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 94A17
Mathematics Subject Classification ID: 62B10
zbMATH DE Number: 2098335
zbMATH Keywords: weak convergence
zbMATH Keywords: \(L_1\)-convergence
zbMATH Keywords: entropy
zbMATH Keywords: Kullback-Leibler distance
zbMATH Keywords: Fisher information
Wikidata QID: Q60522108
reviewed by: Petr Lachout
MaRDI profile type: Publication
cites work: Entropy and the central limit theorem
cites work: The convolution inequality for entropy powers
cites work: Q3943738
cites work: Entropy production by block variable summation and central limit theorems
cites work: Q5829358
cites work: An Information-Theoretic Proof of the Central Limit Theorem with Lindeberg Conditions
cites work: Some inequalities satisfied by the quantities of information of Fisher and Shannon
full work available at URL: s0304-4149(00)00006-5
OpenAlex ID: W1975587666
description: scientific article; zbMATH DE number 2098335