A maximum smoothed likelihood estimator in the current status continuous mark model

TL;DR

This paper introduces a maximum smoothed likelihood estimator for joint distribution functions in a current status continuous mark model, addressing inconsistency issues of the traditional MLE under censored data.

Contribution

It proposes a novel MSLE that is consistent and computationally feasible, improving estimation in current status models with continuous marks.

Findings

MSLE is consistent and well-defined.

The proposed estimator outperforms traditional MLE in simulations.

A simple algorithm for computing MSLE is provided.

Abstract

We consider the problem of estimating the joint distribution function of the event time and a continuous mark variable based on censored data. More specifically, the event time is subject to current status censoring and the continuous mark is only observed in case inspection takes place after the event time. The nonparametric maximum likelihood estimator (MLE) in this model is known to be inconsistent. We propose and study an alternative likelihood based estimator, maximizing a smoothed log-likelihood, hence called a maximum smoothed likelihood estimator (MSLE). This estimator is shown to be well defined and consistent, and a simple algorithm is described that can be used to compute it. The MSLE is compared with other estimators in a small simulation study.