Central limit theorem for dependent multidimensionally indexed random variables

We consider dependent multidimensionally indexed random variables whose dependence is determined by the distance of their indices. This provides a generalization of the well-known notion of m-dependence. For the partial sum of a collection of such variables we prove a central limit theorem.

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Bibliographic Details
Published in:	Statistics & probability letters Vol. 63; no. 1; pp. 67 - 78
Main Authors:	Christofides, Tasos C, Mavrikiou, Petroula M
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier B.V 15-05-2003 Elsevier
Series:	Statistics & Probability Letters
Subjects:	Central limit theorem Dependent random variables Dependent random variables Multidimensionally indexed random variables Central limit theorem Exact sciences and technology Limit theorems Mathematics Multidimensionally indexed random variables Probability and statistics Probability theory and stochastic processes Sciences and techniques of general use Dependent random variables Central limit theorem 60F05 Multidimensionally indexed random variables Characteristic function Dependence Markov inequality Partial sum Probability distribution Dependent variable Random variable Lyapunov type theorem Index theory
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Description
Summary:	We consider dependent multidimensionally indexed random variables whose dependence is determined by the distance of their indices. This provides a generalization of the well-known notion of m-dependence. For the partial sum of a collection of such variables we prove a central limit theorem.
ISSN:	0167-7152 1879-2103
DOI:	10.1016/S0167-7152(03)00054-3