21746 articles – 15574 references  [version française]
 HAL: hal-00117001, version 1
 arXiv: math.ST/0611914
 Available versions: v1 (2006-11-29) v2 (2007-07-28) v3 (2008-04-24)
 Estimation of bivariate excess probabilities for elliptical models
 (2006-11-29)
 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
 Subject : Mathematics/Statistics
 Keyword(s): Conditional excess probability – asymptotic independence – elliptic law.
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 hal-00117001, version 1 http://hal.archives-ouvertes.fr/hal-00117001 oai:hal.archives-ouvertes.fr:hal-00117001 From: Philippe Soulier <> Submitted on: Wednesday, 29 November 2006 13:32:01 Updated on: Wednesday, 29 November 2006 14:13:17