A couple of non reduced bias generalized means in extreme value theory: An asymptotic comparison

Helena Penalva, M. Ivette Gomes, Frederico Caeiro, M. Manuela Neves

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

Lehmer’s mean-of-order p (Lp) generalizes the arithmetic mean, and Lp extreme value index (EVI)-estimators can be easily built, as a generalization of the classical Hill EVI-estimators. Apart from a reference to the asymptotic behaviour of this class of estimators, an asymptotic comparison, at optimal levels, of the members of such a class reveals that for the optimal (p, k) in the sense of minimal mean square error, with k the number of top order statistics involved in the estimation, they are able to overall outperform a recent and promising generalization of the Hill EVI-estimator, related to the power mean, also known as Hölder’s mean-of-order-p. A further comparison with other ‘classical’ non-reduced-bias estimators still reveals the competitiveness of this class of EVI-estimators.

Original languageEnglish
Pages (from-to)281-298
Number of pages18
JournalREVSTAT: Statistical Journal
Volume18
Issue number3
DOIs
Publication statusPublished - Jul 2020

Keywords

  • Heavy tails
  • Optimal tuning parameters
  • Semi-parametric estimation
  • Statistical extreme value theory

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