On the multivariate Hüsler-Reiss distribution attracting the maxima of elliptical triangular arrays

Details

Serval ID
serval:BIB_B5F7937C0742
Type
Article: article from journal or magazin.
Collection
Publications
Title
On the multivariate Hüsler-Reiss distribution attracting the maxima of elliptical triangular arrays
Journal
Statistics & Probability Letters
Author(s)
Hashorva E.
ISSN
0167-7152
Publication state
Published
Issued date
2006
Peer-reviewed
Oui
Volume
76
Number
18
Pages
2027-2035
Language
english
Abstract
Let (X-ln((j)), ..., X-dn((j))), n >= 1, 1 <= j <= n, be a triangular array of independent elliptical random vectors in R-d, d >= 2. In this paper we investigate the asymptotic behaviour of the multivariate maxima of this triangular array. Generalising previous results for the bivariate set-up, we show that the normalised maxima of this elliptical triangular array is attracted by the multivariate Husler-Reiss distribution function provided that the components of the triangular array become asymptotically dependent with a specific rate, and further the random radius pertaining to the elliptical random vectors is in the Gumbel max-domain of attraction.
Keywords
Maxima of triangular arrays, Multivariate elliptical distribution, Multivariate Husler-Reiss distribution, Gumbel max-domain of attraction, Weak convergence
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Create date
03/09/2010 10:43
Last modification date
20/08/2019 15:24
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