Mathematics – Statistics Theory
Scientific paper
2010-01-12
Annals of Statistics 2010, Vol. 38, No. 1, 352-387
Mathematics
Statistics Theory
Published in at http://dx.doi.org/10.1214/09-AOS721 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Scientific paper
10.1214/09-AOS721
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.
Groeneboom Piet
Jongbloed Geurt
Witte Birgit I.
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