Extremes

, Volume 17, Issue 2, pp 337–358 | Cite as

New estimators of the extreme value index under random right censoring, for heavy-tailed distributions

Article

Abstract

This paper presents new approaches for the estimation of the extreme value index in the framework of randomly censored samples, based on the ideas of Kaplan-Meier integration and the synthetic data approach of Leurgans (1987). These ideas are developed here in the heavy-tailed case, and lead to modifications of the Hill estimator, for which the consistency is proved under first order conditions. Simulations exhibit good performances of the two approaches, compared to the only existing adaptation of the Hill estimator in this context

Keywords

Extreme value index Tail inference Random censoring Kaplan-Meier integration 

Mathematical Subject Classifications

62G32 (Extreme value statistics) 62N02 (Estimation for censored data) 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques de Versailles (CNRS UMR 8100)Université de Versailles-Saint-Quentin-en-YvelinesVersailles CedexFrance
  2. 2.UPEMLV, UPECUniversité Paris-Est, Laboratoire d’Analyse et de Mathématiques Appliquées (CNRS UMR 8050)CréteilFrance

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