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We consider the problem of estimating the distribution function, the densityand the hazard rate of the (unobservable) event time in the current statusmodel. A well studied and natural nonparametric estimator for the distributionfunction in this model is the nonparametric maximum likelihood estimator (MLE).We study two alternative methods for the estimation of the distributionfunction, assuming some smoothness of the event time distribution. The firstestimator is based on a maximum smoothed likelihood approach. The second methodis based on smoothing the (discrete) MLE of the distribution function. Theseestimators can be used to estimate the density and hazard rate of the eventtime distribution based on the plug-in principle.

Maximum smoothed likelihood estimation and smoothed maximum likelihood estimation in the current status model