An application of a multivariate central limit theorem to sampling without replacement
type: Item
instance of: scholarly article
title: An application of a multivariate central limit theorem to sampling without replacement
zbMATH Open document ID: 0657.62012
DOI: 10.1016/0047-259X(88)90106-6
author: Donald B. White
published in: Journal of Multivariate Analysis
publication date: 1988-01-01T00:00:00Z
review text: A general multivariate central limit theorem of \textit{M. G. Hahn}, \textit{P. Hahn}, and \textit{M. J. Klass} [Ann. Probab. 11, 277-301 (1983; Zbl 0514.60025)] gives conditions relating the one-dimensional marginals of the summands in an infinitesimal triangular array to those of the limit law. This theorem is applied here to the sample sums obtained by sampling without replacement from a sequence of finite multivariate populations. An important subcase of this result is where the sequence of populations' values are restricted to a finite set. Here the limit laws are shown to be a natural generalization of the multivariate Poisson distribution.
Mathematics Subject Classification ID: 62D05
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 4074177
zbMATH Keywords: infinitely divisible laws
zbMATH Keywords: generalized multivariate hypergeometric distribution
zbMATH Keywords: multivariate central limit theorem
zbMATH Keywords: infinitesimal triangular array
zbMATH Keywords: sampling without replacement
zbMATH Keywords: sequence of finite multivariate populations
zbMATH Keywords: generalization of the multivariate Poisson distribution
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4074177