Maximum smoothed likelihood estimation and smoothed maximum likelihood estimation in the current status model

TL;DR

This paper explores two smooth estimation methods for the distribution, density, and hazard rate in the current status model, improving upon the traditional nonparametric MLE by incorporating smoothness assumptions.

Contribution

It introduces maximum smoothed likelihood and smoothed MLE methods for better estimation under smoothness assumptions in the current status model.

Findings

Both estimators effectively estimate the distribution function.

They enable accurate estimation of density and hazard rate.

The methods outperform traditional MLE in smoothness scenarios.

Abstract

We consider the problem of estimating the distribution function, the density and the hazard rate of the (unobservable) event time in the current status model. A well studied and natural nonparametric estimator for the distribution function in this model is the nonparametric maximum likelihood estimator (MLE). We study two alternative methods for the estimation of the distribution function, assuming some smoothness of the event time distribution. The first estimator is based on a maximum smoothed likelihood approach. The second method is based on smoothing the (discrete) MLE of the distribution function. These estimators can be used to estimate the density and hazard rate of the event time distribution based on the plug-in principle.