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Extremes

, Volume 20, Issue 1, pp 199–237 | Cite as

A general estimator for the right endpoint with an application to supercentenarian women’s records

  • Isabel Fraga AlvesEmail author
  • Cláudia Neves
  • Pedro Rosário
Article

Abstract

We extend the setting of the right endpoint estimator introduced in Fraga Alves and Neves (Statist. Sinica 24, 1811–1835, 2014) to the broader class of light-tailed distributions with finite endpoint, belonging to some domain of attraction induced by the extreme value theorem. This stretch enables a general estimator for the finite endpoint, which does not require estimation of the (supposedly non-positive) extreme value index. A new testing procedure for selecting max-domains of attraction also arises in connection with the asymptotic properties of the general endpoint estimator. The simulation study conveys that the general endpoint estimator is a valuable complement to the most usual endpoint estimators, particularly when the true extreme value index stays above −1/2, embracing the most common cases in practical applications. An illustration is provided via an extreme value analysis of supercentenarian women data.

Keywords

Extreme value theory Semi-parametric estimation Tail estimation Regular variation Monte Carlo simulation Human lifespan 

AMS 2000 Subject Classifications

62G32 62F10 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.CEAUL and DEIO, FCULUniversity of LisbonLisboaPortugal
  2. 2.University of ReadingReadingUK
  3. 3.CEAULUniversity of LisbonLisboaPortugal

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