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

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

Piet Groeneboom, Geurt Jongbloed, and Birgit I. Witte

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

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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Primary Subjects: 62G05, 62N01

Secondary Subjects: 62G20

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

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aos/1262271618
Digital Object Identifier: doi:10.1214/09-AOS721
Zentralblatt MATH identifier: 1181.62157
Mathematical Reviews number (MathSciNet): MR2589325

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