Functional limit theorems for row and column exchangeable arrays
type: Item
instance of: scholarly article
title: Functional limit theorems for row and column exchangeable arrays
zbMATH Open document ID: 0865.60024
published in: Journal of Multivariate Analysis
publication date: 1997-07-07T00:00:00Z
review text: An array \(\{Y_{i,j}:1\leq i\leq m, 1\leq j\leq r\}\) is called a row and column exchangeable (RCE) array if \(\{Y_{i,j}\}\overset {D}=\{Y_{p(i),q(j)}\}\), where \(p\) and \(q\) are arbitrary permutations of \(\{1,\dots,m\}\) and \(\{1,\dots,r\}\), respectively. Assume that \(\{Y^{(n)}_{i,j}:1\leq i\leq m_n, 1\leq j\leq r_n\}\) is a sequence of RCE arrays with \(\{Y_{i,j}\}\overset {D}=\{Y^{(n)}_{\sigma_n(i),\pi_n(j)}\}\). Let \(X_n\) be the process defined on \([0,1]^2\) by \(X_n(s,t)=\sum^{[r_ns]}_{j=1} \sum^{[m_nt]}_{i=1}Y^{(n)}_{i,j}\) with \(X_n(s,0)=X_n(0,t)=0\) for all \((s,t)\in [0,1]^2\). The authors show that the various one- and two-dimensional processes arise as weak limits of the partial sum processes defined by RCE arrays \(\{Y^{(n)}_{i,j}\}\).
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60G09
zbMATH DE Number: 844605
zbMATH Keywords: row and column exchangeable array
zbMATH Keywords: weak convergence
author: B. Gail Ivanoff
author: Neville Weber
reviewed by: Ken-ichi Yoshihara
MaRDI profile type: Publication
full work available at URL: jmva.1995.1071
OpenAlex ID: W2052296370
DOI: 10.1006/JMVA.1995.1071
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description: scientific article; zbMATH DE number 844605