Extreme value theory for multivariate stationary sequences
type: Item
instance of: scholarly article
title: Extreme value theory for multivariate stationary sequences
zbMATH Open document ID: 0679.62039
DOI: 10.1016/0047-259X(89)90028-6
author: Tailen Hsing
published in: Journal of Multivariate Analysis
publication date: 1989-01-01T00:00:00Z
review text: The author considers multivariate extremal type theorems and some related problems in a setting where the assumptions of independence and linear normalization in the classical setting are weakened. For a stationary sequence of random vectors he introduces a distributional mixing condition which is an obvious extension of \textit{M. R. Leadbetter}'s condition \(D(u_ n)\) in the one-dimensional case [Z. Wahrscheinlichkeitstheorie verw. Gebiete 28, 289-303 (1974; Zbl 0265.60019)]. For a sequence satisfying this condition the following topics are studied. (1) To obtain characterizations of the weak limit F of properly normalized partial maxima. (2) To study a condition under which the partial maxima behave as they would if the sequence were i.i.d. (3) To consider problems in connection with the independence of the margins of F.
Mathematics Subject Classification ID: 62H05
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60F99
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 62G30
zbMATH DE Number: 4113766
zbMATH Keywords: multivariate extreme value theory
zbMATH Keywords: stationary sequence
zbMATH Keywords: mixing condition
reviewed by: Toshio Mori
MaRDI profile type: Publication
cites work: Multivariate extreme value distributions for stationary Gaussian sequences
cites work: Max-infinite divisibility
cites work: Convergence to bivariate limiting extreme value distributions
cites work: Limit Theorems for the Maximum Term in Stationary Sequences
cites work: Q5560061
cites work: Maxima and minima of stationary sequences
cites work: Limit laws for the maximum and minimum of stationary sequences
cites work: Q3049592
cites work: Q4179588
cites work: Q4179603
cites work: Q3736730
cites work: Point processes and multivariate extreme values
cites work: Q5819779
cites work: Q4162318
cites work: Limit theory for multivariate sample extremes
cites work: On extreme values in stationary sequences
cites work: Extremes and related properties of random sequences and processes
cites work: A note on the asymptotic independence of high level crossings for dependent Gaussian processes
cites work: Extreme Values in Uniformly Mixing Stationary Stochastic Processes
cites work: Asymptotic Independence of Vector Components of Multivariate Extreme Order Statistics
cites work: Bivariate extreme statistics. I
cites work: Extreme Values in Samples from $m$-Dependent Stationary Stochastic Processes
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description: scientific article; zbMATH DE number 4113766