The rate of convergence in the central limit theorem for non-stationary dependent random vectors
type: Item
instance of: scholarly article
title: The rate of convergence in the central limit theorem for non-stationary dependent random vectors
zbMATH Open document ID: 0646.60023
DOI: 10.1016/0047-259X(88)90074-7
author: Richard Glendinning
published in: Journal of Multivariate Analysis
publication date: 1988-01-01T00:00:00Z
review text: Let \((X_ j\), \(j\geq 1)\) be a strictly stationary sequence of uniformly mixing variables with zero mean, unit variance and finite fourth moments. Consider the vector \(S_ n=\sum^{n}_{j=1}\alpha_{nj}X_ j\) where \(\alpha_{nj}=(\alpha_{nj1}\), \(\alpha_{nj2})'\), \(\alpha_{nj1}\), \(\alpha_{nj2}\in R\) 1 and \(| \alpha_{nj1}| \leq 1,| \alpha_{nj2}| \leq 1\). The author estimates the rate at which \(S_ n\) converges to normality. The extension of this result to bounded R s- valued weights (s\(\geq 1)\) has also been indicated.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G10
zbMATH DE Number: 4054693
zbMATH Keywords: rate of convergence
zbMATH Keywords: uniformly mixing sequences
zbMATH Keywords: strictly stationary sequence
reviewed by: Adhir K. Basu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4054693