# Gaussian approximation of conditional elliptical random vectors

## Details

Serval ID

serval:BIB_70E58497944B

Type

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

Collection

Publications

Institution

Title

Gaussian approximation of conditional elliptical random vectors

Journal

Stochastic Models

ISSN

1532-6349

1532-4214 ([electronic])

1532-4214 ([electronic])

Publication state

Published

Issued date

2006

Peer-reviewed

Oui

Volume

22

Number

3

Pages

441-457

Language

english

Abstract

Let U-d = (U-1,..., U-d)(inverted perpendicular), d >= 2 be a random vector uniformly distributed on the unit sphere of R-d, and let A is an element of R-dxd be a non-singular matrix. Consider an elliptical random vector X = (X-1, ..., X-d)(inverted perpendicular) with stochastic representation RA(inverted perpendicular) U-d where the positive random radius R is independent of U-d, and let X-I = (X-i, i is an element of I)(inverted perpendicular), X-J = (X-i, i is an element of J)(inverted perpendicular) be two vectors with non-empty disjoint index sets I, J, I boolean OR J = {1,..., d}. Motivated by the Gaussian approximation of the conditional distribution of bivariate spherical random vectors obtained in Berman([1]) we derive in this paper a Gaussian approximation for the conditional distribution X-I | X-J = u(J), u is an element of R-d as uJ tends to a boundary point provided that the random radius R has distribution function in the Gumbel max-domain of attraction. Further, we generalise Berman's result to the multivariate elliptical setup.

Keywords

Conditional distribution, Elliptical random vectors, Gaussian approximation, Gumbel max-domain of attraction, Weak convergence

Web of science

Create date

03/09/2010 10:45

Last modification date

20/08/2019 14:29