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