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Modélisation des évènements rares et estimation des quantiles extrêmes, méthodes de sélection de modèles pour les queues de distribution

Abstract : This PhD. work deals with the modelling of rare event and the estimation of extreme quantiles through different models, and with the selection of these models. Extreme value theory allows for nonparametric estimation of distribution tails. Since these estimations are biased, we use usual parametric models. However, these models are estimated and selected by procedures involving the whole sample. The outputs are thus driven by the most likely values of the variables. Therefore, we propose two goodness-of-fit tests for distribution tail, the ET (Exponential Tail) test and the GPD (Generalised Pareto Distribution) test, to select models providing good estimations of the tail (comparing to the POT method). When we wish to have a good picture of the distribution both for the most likely values and for the extreme values, we can first apply a usual goodness-of-fit test to a set of models and then an adequacy test for the distribution tail. When no distribution is accepted by both tests, we propose a Bayesian regularisation procedure which improves the tail fit of a central model (adapted to the most likely values), thanks to an expert opinion concerning the distribution tail. Finally, when we wish to use the POT method, we have to reduce its estimation bias, especially in extreme quantile estimation. Since POT is based on the approximation of the distribution of excesses over a threshold by a GPD distribution, we try to produce a better estimation of this distribution through a Bayesian procedure. The Bayesian estimation of the GPD parameters leads to a reduced estimation bias for extreme quantiles computed from POT, in particular when we introduce an expert opinion concerning the distribution tail.
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https://tel.archives-ouvertes.fr/tel-00004666
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Submitted on : Monday, February 16, 2004 - 10:03:47 AM
Last modification on : Friday, November 6, 2020 - 4:12:39 AM
Long-term archiving on: : Friday, April 2, 2010 - 8:17:34 PM

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  • HAL Id : tel-00004666, version 1

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Myriam Garrido. Modélisation des évènements rares et estimation des quantiles extrêmes, méthodes de sélection de modèles pour les queues de distribution. Modélisation et simulation. Université Joseph-Fourier - Grenoble I, 2002. Français. ⟨tel-00004666⟩

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