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

Citation
Groeneboom, Piet et al., Maximum smoothed likelihood estimation and smoothed maximum likelihood estimation in the current status model, Annals of statistics , 38(1), 2010, pp. 352-387
Journal title
ISSN journal
00905364
Volume
38
Issue
1
Year of publication
2010
Pages
352 - 387
Database
ACNP
SICI code
Abstract
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.