Limit laws for extremes of dependent stationary Gaussian arrays

Détails

ID Serval
serval:BIB_F365CC91F3BA
Type
Article: article d'un périodique ou d'un magazine.
Collection
Publications
Institution
Titre
Limit laws for extremes of dependent stationary Gaussian arrays
Périodique
Statistics & Probability Letters
Auteur(s)
Hashorva E., Weng Z.
ISSN
0167-7152 (Print)
Statut éditorial
Publié
Date de publication
2013
Peer-reviewed
Oui
Volume
83
Numéro
1
Pages
320-330
Langue
anglais
Résumé
In this paper we show that the componentwise maxima of weakly dependent bivariate stationary Gaussian triangular arrays converge in distribution after appropriate normalization to Husler-Reiss distribution. Under a strong dependence assumption, we prove that the limit distribution of the maxima is a mixture of a bivariate Gaussian distribution and Husler-Reiss distribution. An important new finding of our paper is that the componentwise maxima and componentwise minima remain asymptotically independent even in the settings of Husler and Reiss (1989) allowing further for weak dependence. Further we derive an almost sure limit theorem under the Berman condition for the components of the triangular array.
Mots-clé
Husler-Reiss distribution, Brown-Resnick copula, Gumbel max-domain of attraction, Berman condition, Almost sure limit theorem
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Création de la notice
17/09/2012 15:55
Dernière modification de la notice
20/08/2019 16:20
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