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Smooth Plug‐in Inverse Estimators in the Current Status Continuous Mark Model
Author(s) -
GROENEBOOM PIET,
JONGBLOED GEURT,
WITTE BIRGIT I.
Publication year - 2012
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2011.00755.x
Subject(s) - mathematics , estimator , pointwise , censoring (clinical trials) , event (particle physics) , statistics , mathematical analysis , physics , quantum mechanics
. 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.