The Annals of Statistics

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

Piet Groeneboom, Geurt Jongbloed, and Birgit I. Witte

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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.

Article information

Ann. Statist. Volume 38, Number 1 (2010), 352-387.

First available in Project Euclid: 31 December 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G05: Estimation 62N01: Censored data models
Secondary: 62G20: Asymptotic properties

Current status data maximum smoothed likelihood smoothed maximum likelihood distribution estimation density estimation hazard rate estimation asymptotic distribution


Groeneboom, Piet; Jongbloed, Geurt; Witte, Birgit I. Maximum smoothed likelihood estimation and smoothed maximum likelihood estimation in the current status model. Ann. Statist. 38 (2010), no. 1, 352--387. doi:10.1214/09-AOS721.

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