Central limit theorems for sequences with \(m(n)\)-dependent main part
type: Item
instance of: scholarly article
title: Central limit theorems for sequences with \(m(n)\)-dependent main part
zbMATH Open document ID: 0759.60020
DOI: 10.1016/0378-3758(92)90049-X
author: Gert Nieuwenhuis
published in: Journal of Statistical Planning and Inference
publication date: 1993-01-16T00:00:00Z
review text: A triangular array \((X_ i^{(n)}, 1\leq i\leq h(n), n\in N)\) is called \(m(n)\)-dependent if for all \(n\in N\) and \(k\in\{2,\ldots,h(n)-m(n)\}\) the random vectors \((X_ i^{(n)},1\leq i\leq k-1)\) and \((X_ j^{(n)}, m(n)+k\leq j\leq h(n))\) are independent. A triangular array \((X_ i^{(n)})\) is said to have \(m(n)\)-dependent main part \((X_{i,m(n)})\) and a residual part \((\overline X_{i,m(n)})\) if \(X_ i^{(n)}=X_{i,m(n)}+\overline X_{i,m(n)}\) for all \(n\in N\), \(1\leq i\leq h(n)\), and \((X_{i,m(n)})\) is \(m(n)\)-dependent. Under various conditions the central limit theorem for such triangular arrays \((X_ i^{(n)})\) is considered. \textit{K. N. Berk}'s theorem [Ann. Probab. 1, 352-354 (1973; Zbl 0263.60006)] for \(m(n)\)-dependent random variables is used essentially.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 62M10
zbMATH DE Number: 95577
zbMATH Keywords: \(m\)-dependent sequences
zbMATH Keywords: triangular array
zbMATH Keywords: central limit theorem
reviewed by: V. Paulauskas
MaRDI profile type: Publication
cites work: Q5631966
cites work: A central limit theorem for m-dependent random variables with unbounded m
cites work: Q3739966
cites work: Q3827448
cites work: Asymptotic normality of \(L\)-statistics based on \(m(n)\)-decomposable time series
cites work: Q5624460
cites work: Some Concepts of Dependence
cites work: Iterated Limits and the Central Limit Theorem for Dependent Variables
cites work: Some stochastic inequalities and asymptotic normality of serial rank statistics in general linear processes
cites work: A Central Limit Theorem for Multilinear Stochastic Process
cites work: Q3323077
full work available at URL: 0378-3758(92)90049-x
OpenAlex ID: W2067800924
description: scientific article; zbMATH DE number 95577