Maximum smoothed likelihood estimation and smoothed maximum likelihood estimation in the current status model
Piet Groeneboom, Geurt Jongbloed, Birgit I. Witte
The Annals of Statistics · 2010 · Volume 38 · Issue 1
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.
Keywords
62G05, 62G20, 62N01, asymptotic distribution, Current status data, Density estimation, Distribution estimation, hazard rate estimation, maximum smoothed likelihood, smoothed maximum likelihood
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