Limit properties for multivariate extreme values in sequences of independent, non-identically distributed random vectors
type: Item
instance of: scholarly article
title: Limit properties for multivariate extreme values in sequences of independent, non-identically distributed random vectors
zbMATH Open document ID: 0676.62019
DOI: 10.1016/0304-4149(89)90105-1
published in: Stochastic Processes and their Applications
publication date: 1989-01-01T00:00:00Z
review text: Let \(M_ n\) be the vector of componentwise maxima of independent random vectors \(X_ i\), \(1\leq i\leq n\). Let \(a_ n>0\) and \(b_ n\) be such that \((M_ n-b_ n)/a_ n\) converges in distribution to a nondegenerate random vector with df G. In general G can be any df; but not so when each \(X_ i\) is uniformly asymptotic negligible with respect to the norming constants. Under one such condition, the structure of G is characterized, generalizing the univariate discussion in \textit{J. Galambos}, The asymptotic theory of extreme order statistics. 2nd ed. (1987; Zbl 0634.62044), p. 217. Furthermore, the dependence structure of G is analyzed. Conditions are given which ensure that G (i) has independent components, (ii) is max- infinite divisible, (iii) is associated, and (iv) is an extreme value df.
reviewed by: H. N. Nagaraja
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 62H05
zbMATH DE Number: 4107923
zbMATH Keywords: limit of extreme values
zbMATH Keywords: uniform negligibility condition
zbMATH Keywords: independence
zbMATH Keywords: positive lower orthant dependence
zbMATH Keywords: association
zbMATH Keywords: multivariate extremes
zbMATH Keywords: non i.i.d. random vectors
zbMATH Keywords: limit laws
zbMATH Keywords: componentwise maxima of independent random vectors
zbMATH Keywords: dependence structure
zbMATH Keywords: max-infinite divisible
author: J. Hüsler
MaRDI profile type: Publication
full work available at URL: 0304-4149(89)90105-1
OpenAlex ID: W2062024114
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description: scientific article; zbMATH DE number 4107923