Presmoothed Kaplan-Meier and Nelson-Aalen estimators

Abstract

In this article, a modification of the Kaplan-Meier and Nelson-Aalen estimators in the right random censorship model is studied. The new estimators are obtained by replacing the censoring indicator variables in the classical definitions by values of a nonparametric regression estimator. Asymptotic normality is obtained and it is shown that this presmoothing idea leads to a gain in asymptotic mean squared error. A local plug-in bandwidth selector is introduced and the problem of optimal pilot bandwidth selection for this estimator is studied. The gain of the presmoothed estimators with automatic plug-in bandwidth selector is demonstrated in a simulation study.