# Strong invariance principles for tail quantile processes with applications to extreme value index estimation

1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : Many estimators of the extreme value index are functions of the $k_n$ largest observations of the sample and therefore can be seen as a functional of the $k_n$ upper tail quantile process. Under classical second order assumptions, this quantile process can be approximated, via a quantile transformation, by a non linear functional of the tail uniform empirical process. Here, we prove a strong invariance principle for this non linear functional. In some ways, this result improves the approximation result obtained by Drees since it is convenient to prove strong limit theorems. In particular, we obtain a functional law of the iterated logarithm for the quantile process. As an application, we establish a compact law of the iterated logarithm for the classical Hill estimator.
Type de document :
Communication dans un congrès
EVA 2011 - 7th International Conference on Extreme Value Analysis, Jun 2011, Lyon, France. pp.CDROM, 2011
Domaine :

https://hal.archives-ouvertes.fr/hal-00764293
Contributeur : Stephane Girard <>
Soumis le : mercredi 12 décembre 2012 - 16:54:09
Dernière modification le : mercredi 11 avril 2018 - 01:59:02

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• HAL Id : hal-00764293, version 1

### Citation

Stephane Girard, Ludovic Menneteau. Strong invariance principles for tail quantile processes with applications to extreme value index estimation. EVA 2011 - 7th International Conference on Extreme Value Analysis, Jun 2011, Lyon, France. pp.CDROM, 2011. 〈hal-00764293〉

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