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Improved Estimators of Tail Index and Extreme Quantiles under Dependence Serials

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Abstract

In this paper, we deal with the estimation problem for the extreme value parameters in the case of stationary \(\beta\)-mixing serials with heavy-tailed distributions. We first introduce two families of estimators generalizing the Hill’s estimator. And from those families, three asymptotically unbiased estimators of the extreme value index are established. Our reflection is based on the generalized Jackknife methodology which consists of taking any pair of three special cases of our family of estimators to cancel the bias term. The resulting estimators are also used to deduce three asymptotically unbiased estimators of the extreme quantiles. In a simulation survey, the performance of our proposed methods are compared to alternative estimators recently introduced in the literature. Finally, our methods are applied to high financial losses data in order to estimate the Value-at-Risk of the daily stock returns on the S&P500 index.

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ACKNOWLEDGMENTS

The authors would like to thank the Reviewers and editors for their valuable comments and suggestions that helped improve considerably the paper.

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Authors and Affiliations

  1. Laboratoire d’Etudes et de Recherche en Statistiques et Développement, Saint-Louis, Sénégal

    Mamadou Aliou Barry & El Hadji Deme

  2. Département de Mathématiques, Université Alioune Diop de Bambey, Sénégal (Equipe de recherche en Statistique et Modèles Aléatoires (ERESMA)), Bambey, Sénégal

    Aba Diop

  3. Institut Montpelliérain Alexander Grothendieck, UMR CNRS 5149, Place Eugéne Bataillon, 34090, Montpellier, France

    Solym M. Manou-Abi

  4. Centre Universitaire de Formation et de Recherche, Mayotte, France

    Solym M. Manou-Abi

Authors
  1. Mamadou Aliou Barry
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  2. El Hadji Deme
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  3. Aba Diop
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  4. Solym M. Manou-Abi
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Correspondence to El Hadji Deme.

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Barry, M.A., Deme, E.H., Diop, A. et al. Improved Estimators of Tail Index and Extreme Quantiles under Dependence Serials. Math. Meth. Stat. 32, 133–153 (2023). https://doi.org/10.3103/S1066530723020011

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  • DOI: https://doi.org/10.3103/S1066530723020011

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