Semi-parametric random censorship models

Abstract

Starting with an identifying Volterra type integral equation for the survival function under randomly right censored observations, we derive general product type estimators. These general estimators can be specified according to the additional information about the conditional expectation of the indicator given the observation time. Among others, the well-known nonparametric Kaplan-Meier and two semi-parametric estimators are derived. For the latter ones, the conditional expectation of the indicator has to be parameterizable. Some important probabilistic properties of these semi-parametric estimators are reviewed here together with their nonparametric counterparts. In particular, a strong law and asymptotic normality of semi-parametric integrals together with their efficiency are discussed. Furthermore, validation tests for the parametric assumption are considered and bootstrapping under these semi-parametric models is reviewed.