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Journal of Statistical Theory and Practice

, Volume 9, Issue 1, pp 200–218 | Cite as

Revisiting the Maximum Likelihood Estimation of a Positive Extreme Value Index

  • Frederico Caeiro
  • M. Ivette Gomes
Article

Abstract

In this article, we revisit Feuerverger and Hall’s maximum likelihood estimation of the extreme value index. Based on those estimators we propose new estimators that have the smallest possible asymptotic variance, equal to the asymptotic variance of the Hill estimator. The full asymptotic distributional properties of the estimators are derived under a general third-order framework for heavy tails. Applications to a real data set and to simulated data are also presented.

Keywords

Bias estimation Heavy tails Semiparametric estimation Statistics of extremes 

AMS Subject Classification

62G05 62G20 62G32 

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Copyright information

© Grace Scientific Publishing 2015

Authors and Affiliations

  1. 1.Departamento de Matemática, Faculdade de Ciências e TecnologiaUniversidade Nova de LisboaLisboa, CaparicaPortugal
  2. 2.Centro de Estatística e Aplicações, Faculdade de CiênciasUniversidade de LisboaLisbonPortugal

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