Asymptotics of the norm of elliptical random vectors

Details

Serval ID
serval:BIB_51A8DA70E4B3
Type
Article: article from journal or magazin.
Collection
Publications
Title
Asymptotics of the norm of elliptical random vectors
Journal
Journal of Multivariate Analysis
Author(s)
Hashorva E.
ISSN
0047-259X
Publication state
Published
Issued date
2010
Peer-reviewed
Oui
Volume
101
Number
4
Pages
926-935
Language
english
Abstract
In this paper we consider elliptical random vectors X in R(d), d >= 2 with stochastic representation ARU, where R is a positive random radius independent of the random vector U which is uniformly distributed on the unit sphere of R(d) and A is an element of R(dxd) is a given matrix. Denote by parallel to.parallel to the Euclidean norm in R(d), and let F be the distribution function of R. The main result of this paper is an asymptotic expansion of the probability P {parallel to X parallel to > u} for F in the Gumbel or the Weibuli max-domain of attraction. In the special case that X is a mean zero Gaussian random vector our result coincides with the one derived in Husler et al. (2002) [1].
Keywords
Elliptical distribution, Gaussian distribution, Kotz Type distribution, Gumbel max-domain of attraction, Tail approximation, Density convergence, Weak convergence
Web of science
Open Access
Yes
Create date
03/09/2010 9:58
Last modification date
20/08/2019 14:07
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