2011/09/06 by Piet Groeneboom, Geurt Jongbloed, Groeneboom, Piet +4
Computer Science · Mathematics · #62G05 #62G20 #62H12 #62N02 #Applications (stat.AP) #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #FOS: Mathematics #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #msc:62G05 #msc:62G20 #msc:62H12 #msc:62N02 #stat.AP #stat.TH
paper · pdf · doi:10.48550/arxiv.1109.1172
24 pages, 6 figures
arxiv created 2011/09/06 · openalex publication_date 2011/09/06 · arxiv updated 2011/09/07 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
We consider the problem of estimating the joint distribution function of the event time and a continuous mark variable based on censored data. More specifically, the event time is subject to current status censoring and the continuous mark is only observed in case inspection takes place after the event time. The nonparametric maximum likelihood estimator (MLE) in this model is known to be inconsistent. We propose and study an alternative likelihood based estimator, maximizing a smoothed log-likelihood, hence called a maximum smoothed likelihood estimator (MSLE). This estimator is shown to be well defined and consistent, and a simple algorithm is described that can be used to compute it. The MSLE is compared with other estimators in a small simulation study.