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

TL;DR

This paper introduces smooth plug-in inverse estimators for the joint distribution of event time and a continuous mark in a current status model with interval censoring, providing their asymptotic properties.

Contribution

It proposes two new smooth estimators for a complex censored data model, addressing the inconsistency of the nonparametric maximum likelihood estimator.

Findings

Derived the asymptotic distribution of the estimators

Showed the estimators are consistent and asymptotically normal

Provided theoretical foundation for practical application

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.