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

Journal article (2010)
Department
Delft Institute of Applied Mathematics (EEMCS) (TU Delft)
Copyright: © 2010 Groeneboom, P.; Jongbloed, G.; Witte, B.I. ; Institute of Mathematical Statistics
DOI: https://doi.org/doi:10.1214/09-AOS721
Density estimation Asymptotic distribution Current status data Maximum smoothed likelihood Smoothed maximum likelihood Distribution estimation Hazard rate estimation
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Published Date

01-02-2010

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Source:

Annals of Statistics, 38 (1), 2010

ISSN:

0091-1798

Source:

http://projecteuclid.org/euclid.aos/1262271618

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

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.

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