21734 articles – 15570 references  [version française]
 HAL: hal-00117001, version 2
 arXiv: math/0611914
 Estimation of bivariate excess probabilities for elliptical modelsAbdous B. et alhttp://hal.archives-ouvertes.fr/hal-00117001
 Available versions: v1 (2006-11-29) v2 (2007-07-28) v3 (2008-04-24)
Preprint, Working Paper, ...
Mathematics/Statistics
Estimation of bivariate excess probabilities for elliptical models
Belkacem Abdous () 1, Anne-Laure Fougères () 2, Kilani Ghoudi () 3, Philippe Soulier () 2
 1: Département de médecine sociale et préventive (DMPS) http://w3.fmed.ulaval.ca/dmsp/accueil/ Université Laval Département de Médecine sociale et préventive Faculté de Médecine 2180 Chemin Sainte-Foy Pavillon de l'Est, bureau 1108 Université Laval Québec (Québec), Canada, G1K 7P4 Canada 2: Modélisation aléatoire de Paris X (MODAL'X) http://www.u-paris10.fr/MODALX/0/fiche___laboratoire/ Université Paris X - Paris Ouest Nanterre La Défense France 3: College of Business and Economics Statistics Department (CBE STAT) http://www.cbe.uaeu.ac.ae/Academics/Departments/stat/index.htm United Arab Emirates University College of Business & Economics, UAE University, POB 17555 United Arab Emirates
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.
English

Conditional excess probability – asymptotic independence – elliptic law.
AMS 62G32, 60G70

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 elsart.cls(55.1 KB)
 kotz-1-theta.eps(20 KB)
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 lognormal-theta.eps(19.7 KB)
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 quantile.eps(18.4 KB)
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 afgsrev.ps(312.7 KB)
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 hal-00117001, version 2 http://hal.archives-ouvertes.fr/hal-00117001 oai:hal.archives-ouvertes.fr:hal-00117001 From: Philippe Soulier <> Submitted on: Saturday, 28 July 2007 00:15:07 Updated on: Saturday, 28 July 2007 07:53:51