On the asymptotic joint distribution of an unbounded number of sample extremes
type: Item
instance of: scholarly article
title: On the asymptotic joint distribution of an unbounded number of sample extremes
zbMATH Open document ID: 0627.62023
DOI: 10.1007/BF00718033
author: Ishay Weissman
publication date: 1988-01-01T00:00:00Z
review text: Convergence of the sample maximum to a nondegenerate random variable, as the sample size \(n\to \infty\), implies the convergence in distribution of the k largest sample extremes to a k-dimensional random vector \(M_ k\), for all fixed k. If we let \(k=k(n)\to \infty\), k/n\(\to 0\), then a question arises in a natural way: how fast can k grow so that asymptotic probability statements are unaffected when sample extremes are replaced by \(M_ k\). We answer this question for two classes of events - the class of all Lebesgue sets in \(R^ k\) and the class of events of the form \(\{x\in R^ k\), \(\sum ^{k}_{1}x_ i\leq a\}\).
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 60F99
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 62G30
zbMATH DE Number: 4020201
zbMATH Keywords: asymptotic joint distribution
zbMATH Keywords: unbounded number of sample extremes
zbMATH Keywords: convergence of the sample maximum
zbMATH Keywords: Lebesgue sets
zbMATH Keywords: convergence in total variation
zbMATH Keywords: extreme value distributions
zbMATH Keywords: intermediate order statistics
zbMATH Keywords: multivariate extremal distributions
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4020201