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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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.

Article information

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

Dates
First available in Project Euclid: 31 December 2009

Permanent link to this document
https://projecteuclid.org/euclid.aos/1262271618

Digital Object Identifier
doi:10.1214/09-AOS721

Mathematical Reviews number (MathSciNet)
MR2589325

Zentralblatt MATH identifier
1181.62157

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

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

Citation

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


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