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

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.

Published in at http://dx.doi.org/10.1214/09-AOS721 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (1)

• Maximum likelihood estimation of a log-concave density and its distribution function: Basic properties and uniform consistency

Cited by in corpus (4)

• Likelihood based inference for current status data on a grid: A boundary phenomenon and an adaptive inference procedure
• Maximum smoothed likelihood estimators for the interval censoring model
• Valid and Approximately Valid Confidence Intervals for Current Status Data
• Confidence intervals for intentionally biased estimators