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Estimation of the second order parameter for heavy-tailed distributions

El Hadji Deme 1, 2, * Laurent Gardes 3 Stéphane Girard 1
* Corresponding author
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
2 Lerstad
LERSTAD - laboratoire d'Etudes et de recherches en Statistiques et Développement
Abstract : The extreme-value index is an important parameter in extreme-value theory since it controls the first order behavior of the distribution tail. Numerous estimators of this parameter have been proposed especially in the case of heavy-tailed distributions, which is the situation considered here. Most of these estimators depend on the largest observations of the underlying sample. Their bias is controlled by the second order parameter. In order to reduce the bias of extreme-value index estimators or to select the best number of observations to use, the knowledge of the second order parameter is essential. We propose a simple approach to estimate the second order parameter leading to both existing and new estimators. We establish a general result that can be used to easily prove the asymptotic normality of a large number of estimators proposed in the literature or to compare different estimators within a given family. Some illustrations on simulations are also provided.
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Conference papers
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https://hal.inria.fr/hal-00915698
Contributor : Stephane Girard Connect in order to contact the contributor
Submitted on : Monday, December 9, 2013 - 11:39:33 AM
Last modification on : Tuesday, October 19, 2021 - 11:13:06 PM

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  • HAL Id : hal-00915698, version 1

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El Hadji Deme, Laurent Gardes, Stéphane Girard. Estimation of the second order parameter for heavy-tailed distributions. ERCIM 2013 - 6th International Conference of the ERCIM WG on Computational and Methodological Statistics, Dec 2013, London, United Kingdom. ⟨hal-00915698⟩

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