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Rate of convergence for the generalized Pareto approximation of the excesses

Part of: Stochastic processes Nonparametric inference

Published online by Cambridge University Press:  01 July 2016

J.-P. Raoult  and
R. Worms
J.-P. Raoult*
Affiliation:
Université de Marne-la-Vallée
R. Worms*
Affiliation:
Université de Marne-la-Vallée
*
∗ Postal address: Université de Marne-la-Vallée, Equipe d'Analyse et de Mathématiques appliquées, 5, boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée Cedex 2, France.
∗ Postal address: Université de Marne-la-Vallée, Equipe d'Analyse et de Mathématiques appliquées, 5, boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée Cedex 2, France.
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Abstract

Let F be a distribution function in the domain of attraction of an extreme-value distribution Hγ. If Fu is the distribution function of the excesses over u and Gγ the distribution function of the generalized Pareto distribution, then it is well known that Fu(x) converges to Gγ(x/σ(u)) as u tends to the end point of F, where σ is an appropriate normalizing function. We study the rate of (uniform) convergence to 0 of F̅u(x)-G̅γ((x+u-α(u))/σ(u)), where α and σ are two appropriate normalizing functions.

Keywords

Generalized Pareto distributionexcessesrate of convergence

MSC classification

Primary: 60G70: Extreme value theory; extremal processes
Secondary: 62G20: Asymptotic properties
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 35 , Issue 4 , December 2003 , pp. 1007 - 1027
Copyright
Copyright © Applied Probability Trust 2003 

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