Canonical row-column-exchangeable arrays
type: Item
instance of: scholarly article
title: Canonical row-column-exchangeable arrays
zbMATH Open document ID: 0548.60039
DOI: 10.1016/0047-259X(84)90072-1
author: N. E. Zubov
published in: Journal of Multivariate Analysis
publication date: 1984-01-01T00:00:00Z
review text: It has been shown by \textit{D. J. Aldous} [ibid. 11, 581-598 (1981; Zbl 0474.60044)] that a row-column-exchangeable array \((X_{ij}:\) i,\(j\geq 1)\) of random variables is equivalent in distribution to a standard array of the form \((X^*_{ij})=(f(\alpha,\xi_ i,\eta_ j,\lambda_{ij}))\), where f is a Borel function and \(\alpha,\xi_ i,\eta_ j,\lambda_{ij},i,j=1,2,..\). are independent uniformly distributed random variables. It is shown here that there exists a canonical version \((X'_{ij})=(g(\alpha',\xi '_ i,\eta '_ j,\lambda'_{ij}))\) such that the \(X'_{ij}\)'s and the \(\sigma\)-field \({\mathcal F}'= \sigma(\alpha',\xi'_ i,\eta'_ j: i,j\geq 1)\) are conditionally independent, given the shell \(\sigma\)-field \(\cap_{n>o}\sigma(X'_{ij}: \max(i,j)>n)\). (The result is mis-stated in the text). This statement, though weaker than Aldous's analogous result for the original array is easier to prove and is sufficient for certain characterisation purposes. The proofs rely on Aldous's constructions.
Mathematics Subject Classification ID: 60G09
zbMATH DE Number: 3874328
zbMATH Keywords: row-column-exchangeable array
reviewed by: F. Papangelou
MaRDI profile type: Publication
cites work: Representations for partially exchangeable arrays of random variables
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description: scientific article; zbMATH DE number 3874328