MAXIMUM SMOOTHED LIKELIHOOD ESTIMATION AND SMOOTHED MAXIMUM LIKELIHOOD ESTIMATION IN THE CURRENT STATUS MODEL

• 成果类型: Article
• 署名作者: Groeneboom, Piet; Jongbloed, Geurt; Witte, Birgit I.
• 署名单位: Delft University of Technology
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/09-AOS721
• 发表日期: 2010
• 页码: 352-387
• 关键词: Bandwidth selection; density

摘要

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 (MILE). 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 oil 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.