  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.
