New estimators of the extreme value index under random right censoring, for heavy-tailed distributions
Résumé
This paper presents new approaches for the estimation of the extreme value index in the framework of randomly censored (from the right) samples, based on the ideas of Kaplan-Meier integration and the synthetic data approach of S.Leurgans (1987). These ideas are developed here in the heavy tail case and for the adaptation of the Hill estimator, for which the consistency is proved under first order conditions. Simulations show good performance of the two approaches, with respect to the only existing adaptation of the Hill estimator in this context.
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