## Extremes of conditioned elliptical random vectors

### Details

Serval ID

serval:BIB_590EAE02369C

Type

**Article**: article from journal or magazin.

Collection

Publications

Fund

Title

Extremes of conditioned elliptical random vectors

Journal

Journal of Multivariate Analysis

ISSN

0047-259X

Publication state

Published

Issued date

2007

Peer-reviewed

Oui

Volume

98

Number

8

Pages

1583-1591

Language

english

Abstract

Let {X-n, n >= 1} be iid elliptical random vectors in R-d, d >= 2 and let I, J be two non-empty disjoint index sets. Denote by X-n ,X- I, X-n ,X- J the subvectors of X-n with indices in I, J, respectively. For any a is an element of R-d such that a(J) is in the support of X (1, J) the conditional random sample X-n,X- I vertical bar X-n,X- J = a (J), n >= 1 consists of elliptically distributed random vectors. In this paper we investigate the relation between the asymptotic behaviour of the multivariate extremes of the conditional sample and the unconditional one. We show that the asymptotic behaviour of the multivariate extremes of both samples is the same, provided that the associated random radius of X, has distribution function in the max-domain of attraction of a univariate extreme value distribution.

Keywords

Elliptical random vectors, Conditional distribution, Multivariate extremes, Max-domain of attraction, Weak convergence, Tail asymptotics

Web of science

Create date

03/09/2010 11:35

Last modification date

30/03/2017 15:05