Mathematics – Statistics Theory
Scientific paper
2011-02-09
Mathematics
Statistics Theory
29 pages, 12 figures
Scientific paper
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 nonparametric 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.
Groeneboom Piet
Jongbloed Geurt
Witte Birgit
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