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Extremes

, Volume 19, Issue 4, pp 561–589 | Cite as

Mean-of-order p reduced-bias extreme value index estimation under a third-order framework

  • Frederico Caeiro
  • M. Ivette Gomes
  • Jan Beirlant
  • Tertius de Wet
Article

Abstract

Reduced-bias versions of a very simple generalization of the ‘classical’ Hill estimator of a positive extreme value index (EVI) are put forward. The Hill estimator can be regarded as the logarithm of the mean-of-order-0 of a certain set of statistics. Instead of such a geometric mean, it is sensible to consider the mean-of-order-p (MOP) of those statistics, with p real. Under a third-order framework, the asymptotic behaviour of the MOP, optimal MOP and associated reduced-bias classes of EVI-estimators is derived. Information on the dominant non-null asymptotic bias is also provided so that we can deal with an asymptotic comparison at optimal levels of some of those classes. Large-scale Monte-Carlo simulation experiments are undertaken to provide finite sample comparisons.

Keywords

Bias estimation Heavy tails Optimal levels Semi-parametric reduced-bias estimation Statistics of extremes 

AMS 2000 Subject Classifications

Primary 62G32 Secondary 65C05 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.CMA and DM, FCTUniversidade Nova de LisboaLisbonPortugal
  2. 2.CEAUL and DEIO, FCULUniversidade de LisboaLisbonPortugal
  3. 3.KU LeuvenLeuvenBelgium
  4. 4.University of the Free StateBloemfonteinSouth Africa
  5. 5.Stellenbosch UniversityStellenboschSouth Africa

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