Bernoulli

  • Bernoulli
  • Volume 14, Number 4 (2008), 1065-1088.

Estimation of bivariate excess probabilities for elliptical models

Belkacem Abdous, Anne-Laure Fougères, Kilani Ghoudi, and Philippe Soulier

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Abstract

Let $(X, Y)$ be a random vector whose conditional excess probability $θ(x, y):=P(Y≤y | X>x)$ 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 $θ(x, y)$ for fixed $x, y$, with $x$ large. They respectively make use of an approximation result of Abdous et al. (cf. Canad. J. Statist. 33 (2005) 317–334, Theorem 1), a new second order refinement of Abdous et al.’s Theorem 1, and a non-approximating method. The estimation of the conditional quantile function $θ(x, ⋅)^←$ for large fixed $x$ is also addressed and these methods are compared via simulations. An illustration in the financial context is also given.

Article information

Source
Bernoulli, Volume 14, Number 4 (2008), 1065-1088.

Dates
First available in Project Euclid: 6 November 2008

Permanent link to this document
https://projecteuclid.org/euclid.bj/1225980571

Digital Object Identifier
doi:10.3150/08-BEJ140

Mathematical Reviews number (MathSciNet)
MR2543586

Zentralblatt MATH identifier
1155.62042

Keywords
asymptotic independence conditional excess probability elliptic law financial contagion rapidly varying tails

Citation

Abdous, Belkacem; Fougères, Anne-Laure; Ghoudi, Kilani; Soulier, Philippe. Estimation of bivariate excess probabilities for elliptical models. Bernoulli 14 (2008), no. 4, 1065--1088. doi:10.3150/08-BEJ140. https://projecteuclid.org/euclid.bj/1225980571


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