# A new semi-parametric family of estimators for the second order parameter

2 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 : An important parameter in extreme value theory is the extreme value index $\gamma$. It controls the fi rst order behavior of the distribution tail. In the literature, numerous estimators of this parameter have been proposed especially in the case of heavy tailed distributions (which is the situation considered here). The most known estimator was proposed by [2]. It depends on the $k$ largest observations of the underlying sample. The bias of the tail index estimator is controlled by the second order parameter $\rho$. In order to reduce the bias of $\gamma$'s estimators or to select the best number $k$ of observations to use, the knowledge of $\rho$ is essential. Some estimators of $\rho$ can be found in the literature, see for example [1, 2, 3]. We propose a semiparametric family of estimators for $\rho$ that encompasses the three previously mentioned estimators. The asymptotic normality of these estimators is then proved in an uni fied way. New estimators of $\rho$ are also introduced.
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-00764313
Contributeur : Stephane Girard <>
Soumis le : mercredi 12 décembre 2012 - 16:57:38
Dernière modification le : mercredi 11 avril 2018 - 01:58:46

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• HAL Id : hal-00764313, version 1

### Citation

El Hadji Deme, Laurent Gardes, Stephane Girard. A new semi-parametric family of estimators for the second order parameter. EVA 2011 - 7th International Conference on Extreme Value Analysis, Jun 2011, Lyon, France. pp.CDROM, 2011. 〈hal-00764313〉

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