Smooth Plug-in Inverse Estimators in the Current Status Continuous Mark Model

• Published in: Scandinavian journal of statistics Vol. 39; no. 1; pp. 15 - 33
• Main Authors: GROENEBOOM, PIET, JONGBLOED, GEURT, WITTE, BIRGIT I.
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.03.2012; Blackwell Publishing; Danish Society for Theoretical Statistics
• Series: Scandinavian Journal of Statistics
• Subjects: asymptotic distribution; Asymptotic methods; bivariate kernel estimation; Censorship; consistency; continuous mark variable; current status data; Data smoothing; Density; Density estimation; Distribution functions; Estimating techniques; Estimators; Mathematical analysis; Maximum likelihood estimation; Musical intervals; Normal distribution; plug-in estimation; Statistical discrepancies; Studies; Vaccination; Variables
• ISSN: 0303-6898; 1467-9469
• DOI: 10.1111/j.1467-9469.2011.00755.x

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.