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.