hal-00634573, version 2

On the estimation of the second order parameter for heavy-tailed distributions

El Hadji Deme ^1, 2, Laurent Gardes () ³, Stephane Girard () ⁴

(2011-10-21)

• 1:  INRIA Rhône-Alpes (INRIA Grenoble Rhône-Alpes)
• http://www.inrialpes.fr/
  INRIA ZIRST 655 Avenue de l'Europe Montbonnot 38334 Saint Ismier cedex France
• 2:  laboratoire d'Etudes et de recherches en Statistiques et Développement (LERSTAD)
• 
  Université Gaston Bergé Sénégal Université Gaston Berger Saint-Louis Sénégal Senegal
• 3:  Institut de Recherche Mathématique Avancée (IRMA)
• http://www-irma.u-strasbg.fr/
  CNRS : UMR7501 – Université de Strasbourg 7 rue René-Descartes, 67084 Strasbourg Cedex, France France
• 4:  MISTIS (INRIA Grenoble Rhône-Alpes / LJK Laboratoire Jean Kuntzmann)
• http://mistis.inrialpes.fr/index.html
  INRIA – Laboratoire Jean Kuntzmann France

Available versions :  v1 (2011-10-21) v2 (2012-05-16) v3 (2012-10-05) v4 (2012-11-16)

Bibliographic reference

• Type of document: Documents without publication reference (Preprint)
• Subject:

  Mathematics/Statistics

  Statistics/Statistics Theory

• Title: On the estimation of the second order parameter for heavy-tailed distributions
• Abstract: The extreme-value index is an important parameter in extreme-value theory since 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. Most of these estimators depend on the k 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 k of observations to use, the knowledge of the second order parameter is essential. In this paper, 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 di erent estimators within a given family. Some illustrations on simulations are also provided.
• Fulltext language: English
• Production date: 2011-10-21

Attached file list to this document: 

• hal-00634573, version 2
• http://hal.archives-ouvertes.fr/hal-00634573
• oai:hal.archives-ouvertes.fr:hal-00634573
• From: Laurent Gardes <>
• Submitted on: Wednesday, 16 May 2012 11:40:43
• Updated on: Wednesday, 16 May 2012 11:56:18