Asymptotics of dominated Gaussian maxima
type: Item
instance of: scholarly article
title: Asymptotics of dominated Gaussian maxima
zbMATH Open document ID: 1035.60051
DOI: 10.1023/A:1025124225680
author: Enkelejd Hashorva
published in: Extremes
publication date: 2004-03-16T00:00:00Z
review text: Let \(\{X_{n}, n\geq1\}\) be a sequence of independent Gaussian random vectors in \(R^{d}, d\geq2\), with common distribution function. The author studies the asymptotic behavior of the probability that for given \(n\in N\) some \(d\)-dimensional Gaussian random vector \(Y_{n}\) dominates the sample maximum \(M_{n}:= (\max_{1\leq i\leq n}X_{i1},\ldots, \max_{1\leq i\leq n}X_{id})\), i.e. \(\text{Pr}\{M_{n}\leq Y_{n}\}\) as \(n\to\infty\). The paper deals with the following cases: \(Y_{n}=a_{n}Z+b_{n}\) and \(Y_{n}=a_{n}X_{1}+b_{n}\) with \(a_{n}\in R_{+}^{d}, b_{n}\in R^{d}\) and \(Z\) is another Gaussian random vector in \(R^{d}\), independent of \(\{X_{n}, n\geq1\}\).
reviewed by: Aleksandr D. Borisenko
Mathematics Subject Classification ID: 60G70
zbMATH DE Number: 2059074
zbMATH Keywords: asymptotics
zbMATH Keywords: dominated Gaussian maxima
zbMATH Keywords: exact asymptotic
MaRDI profile type: Publication
Recommended article: Asymptotic expansions for the distribution of the maximum of Gaussian random fields
Recommended article: Asymptotic domination of sample maxima
Recommended article: Asymptotics of Maxima of Strongly Dependent Gaussian Processes
Recommended article: Q4255178
Recommended article: Q3725261
Recommended article: On the asymptotic distribution of the maximum of a stationary Gaussian sequence
Recommended article: An asymptotic expansion for the distribution of the maximum of a class of Gaussian fields
Recommended article: An asymptotic bound for the tail of the distribution of the maximum of a Gaussian process
Recommended article: Q3330235
Recommended article: Asymptotic behaviour of near-maxima of Gaussian sequences
description: scientific article; zbMATH DE number 2059074