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Activity Number: 538
Type: Contributed
Date/Time: Wednesday, August 7, 2013 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract - #309027
Title: Asymptotic Efficiency of Integral Estimators in the Semiparametric Random Censorship Model
Author(s): Gerhard Dikta*+
Companies: Fachhochschule Aachen
Keywords: semi-parametric ; information bound ; asymptotically efficient ; survival analysis ; Kaplan-Meier estimator ; random censorship model
Abstract:

We study the estimation of integrals of Borel-measurable functions with respect to some unknown lifetime distribution. The observations are assumed to be generated under the semi-parametric random censorship model (SRCM), that is, a random censorship model where the conditional expectation of the censoring indicator given the observation belongs to a parametric family. Under this setup a semi-parametric estimator of the survival function was introduced by the author. If the parametric model assumption is correct, it is known that the integral estimator based on this semi-parametric estimator is at least as efficient as the corresponding nonparametric Kaplan-Meier integral estimator with respect to the asymptotic variance. In this paper we show that the semi-parametric integral estimator is asymptotically efficient with respect to the class of all regular, asymptotically linear estimators under SCRM.


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