B0523
Title: Extreme value index estimation for randomly censored data with competing risks
Authors: Julien Worms - University of Versailles-Saint-Quentin / University Paris-Saclay (France) [presenting]
Rym Worms - University Paris-Est Creteil (France)
Abstract: The study of the tails of (randomly and independently) right-censored data has attracted some attention in the recent years. Concerning the estimation of the extreme value index (e.v.i.) of such data, a strategy consists in using a trick which relates the e.v.i. of the censored sample to the e.v.i. of the complete sample and the probability of not being censored in the tail. We recently proposed an alternative method which, in the context of heavy tail data, led to an adaptation of the famous Hill estimator taking the form of a Kaplan-Meier functional : it weights the data in the tail in a natural way in this survival analysis framework. We extend this method to the case where competing risks are present: in order to estimate useful extreme quantiles, the target is now the e.v.i. of one of the cause-specific survival functions (also called cumulative incidence functions, assumed here to have heavy tails). The proposed estimator is now a functional of the Aalen-Johansen estimator. Note that in this context, it does not seem possible to rely on the trick previously referred to (the first strategy, when there is only one cause). Finite sample behavior and asymptotic properties of the estimator (consistency and asymptotic normality) will be discussed.
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