Article ID: | iaor2012760 |
Volume: | 39 |
Issue: | 1 |
Start Page Number: | 15 |
End Page Number: | 33 |
Publication Date: | Mar 2012 |
Journal: | Scandinavian Journal of Statistics |
Authors: | Jongbloed Geurt, Groeneboom Piet, Witte Birgit I |
Keywords: | estimation, maximum likelihood estimation |
We consider the problem of estimating the joint distribution function of the event time and a continuous mark variable when the event time is subject to interval censoring case 1 and the continuous mark variable is only observed in case the event occurred before the time of inspection. The non-parametric maximum likelihood estimator in this model is known to be inconsistent. We study two alternative smooth estimators, based on the explicit (inverse) expression of the distribution function of interest in terms of the density of the observable vector. We derive the pointwise asymptotic distribution of both estimators.