A Couple of Non Reduced Bias Generalized Means in Extreme Value Theory

An Asymptotic Comparison

Authors

  • Helena Penalva Instituto Politécnico de Setúbal
  • M. Ivette Gomes Universidade de Lisboa
  • Frederico Caeiro Universidade Nova de Lisboa
  • M. Manuela Neves Universidade de Lisboa

DOI:

https://doi.org/10.57805/revstat.v18i3.301

Keywords:

heavy tails, optimal tuning parameters, semi-parametric estimation, statistical extreme value theory

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 H¨older’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.

Published

2020-08-04

How to Cite

Penalva , H., Gomes , M. I., Caeiro , F., & Neves , M. M. (2020). A Couple of Non Reduced Bias Generalized Means in Extreme Value Theory: An Asymptotic Comparison. REVSTAT-Statistical Journal, 18(3), 281–298. https://doi.org/10.57805/revstat.v18i3.301

Most read articles by the same author(s)

<< < 2 3