HAL : hal-00117001, version 3

arXiv : math/0611914

DOI : 10.3150/08-BEJ140

Fiche détaillée

Récupérer au format BibTeX - EndNote - TEI - RefWorks -

Bernoulli 14, 4 (2008) 1065-1088

Versions disponibles :

v1 (29-11-2006)

v2 (28-07-2007)

v3 (24-04-2008)

Estimation of bivariate excess probabilities for elliptical models

Belkacem Abdous 1, Anne-Laure Fougères 2, Kilani Ghoudi 3, Philippe Soulier 2

(11/2008)

Let $(X,Y)$ be a random vector whose conditional excess probability $ \theta(x,y) := P(Y \leq y ~ | \; X >x)$ is of interest. Estimating this kind of probability is a delicate problem as soon as $x$ tends to be large, since the conditioning event becomes an extreme set. Assume that $(X,Y)$ is elliptically distributed, with a rapidly varying radial component. In this paper, three statistical procedures are proposed to estimate $\theta(x,y)$, for fixed $x,y$, with $x$ large. They respectively make use of an approximation result of Abdous {\it et al.} (cf. \citet[Theorem 1]{AFG05}), a new second-order refinement of Abdous {\it et al.}'s Theorem 1, and a non-approximating method. The estimation of the conditional quantile function $\theta(x, \cdot)^\leftarrow$ for large fixed $x$ is also addressed, and these methods are compared via simulations.

1 :	Département de médecine sociale et préventive (DMPS)
	Université Laval
2 :	Modélisation aléatoire de Paris X (MODAL'X)
	Université Paris X - Paris Ouest Nanterre La Défense
3 :	College of Business and Economics Statistics Department (CBE STAT)
	United Arab Emirates University

Domaine

:

Mathématiques/Statistiques Statistiques/Théorie

Mots Clés : Conditional excess probability – asymptotic independence – elliptic law.

hal-00117001, version 3

http://hal.archives-ouvertes.fr/hal-00117001

oai:hal.archives-ouvertes.fr:hal-00117001

Contributeur : Philippe Soulier <>

Soumis le : Jeudi 24 Avril 2008, 17:02:54

Dernière modification le : Mardi 6 Janvier 2009, 12:45:16