Smooth plug-in inverse estimators in the current status continuous mark model

2011/02/09 by Piet Groeneboom, Geurt Jongbloed, Groeneboom, Piet +3
Mathematics · #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1102.1875

29 pages, 12 figures

arxiv created 2011/02/09 · arxiv updated 2011/02/10

Abstract

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.

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