Revisiting the maximum likelihood estimation of a positive extreme value index

Frederico Caeiro, M. Ivette Gomes

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

In this article, we revisit Feuerverger and Halls 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.

Original languageEnglish
Pages (from-to)200-218
Number of pages19
JournalJournal of Statistical Theory and Practice
Volume9
Issue number1
DOIs
Publication statusPublished - 13 Jan 2015

Keywords

  • Bias estimation
  • Heavy tails
  • Semiparametric estimation
  • Statistics of extremes

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