A maximum smoothed likelihood estimator in the current status continuous mark model

Details A maximum smoothed likelihood estimator in the current status continuous mark model A maximum smoothed likelihood estimator in the current status continuous mark model

2011-09-06

arxiv.org/abs/1109.1172v1

Mathematics

Statistics Theory

24 pages, 6 figures

Scientific paper

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.

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