# Gaussian approximation of conditional elliptical random vectors

## Détails

ID Serval
serval:BIB_70E58497944B
Type
Article: article d'un périodique ou d'un magazine.
Collection
Publications
Titre
Gaussian approximation of conditional elliptical random vectors
Périodique
Stochastic Models
ISSN
1532-6349
1532-4214 ([electronic])
Statut éditorial
Publié
Date de publication
2006
Peer-reviewed
Oui
Volume
22
Numéro
3
Pages
441-457
Langue
anglais
Résumé
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.
Mots-clé
Conditional distribution, Elliptical random vectors, Gaussian approximation, Gumbel max-domain of attraction, Weak convergence
Web of science
Création de la notice
03/09/2010 10:45
Dernière modification de la notice
20/08/2019 14:29
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