## 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.

Original language | English |
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Pages (from-to) | 1065-1088 |

Number of pages | 24 |

Journal | Bernoulli |

Volume | 14 |

Issue number | 4 |

DOIs | |

Publication status | Published - Nov 2008 |

## Keywords

- Asymptotic independence
- Conditional excess probability
- Elliptic law
- Financial contagion
- Rapidly varying tails

## ASJC Scopus subject areas

- Statistics and Probability