The central limit theorem for exchangeable random variables without moments
type: Item
instance of: scholarly article
title: The central limit theorem for exchangeable random variables without moments
zbMATH Open document ID: 0619.60024
author: Michael J. Klass
author: Henry Teicher
published in: The Annals of Probability
publication date: 1987-01-01T00:00:00Z
review text: The paper deals with the question of existence of sequences \(a_ n\), \(0<b_ n\to \infty\) such that \[ (*)\quad b_ n^{-1}(X_ 1+X_ 2+...+X_ n-a_ n)\to N(0,1), \] where \(\{X_ n: n\geq 1\}\) is a sequence of exchangeable r.v.'s. The authors have proved that (*) implies that \(b_ n/n^{\alpha}\) must be slowly varying with \(\alpha =1/2\) or 1. Also necessary and sufficient conditions for (*) have been found.
reviewed by: Zbigniew J. Jurek
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G09
zbMATH DE Number: 4005236
zbMATH Keywords: central limit theorem
zbMATH Keywords: tightness
zbMATH Keywords: exchangeable
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992260
OpenAlex ID: W1965691544
DOI: 10.1214/AOP/1176992260
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description: scientific article; zbMATH DE number 4005236