Estimators for the interval censoring problem

TL;DR

This paper compares three estimators for the interval censoring case 2 problem, analyzing their asymptotic distributions and performance through simulations to determine their effectiveness in statistical estimation.

Contribution

It introduces and compares a histogram-type estimator, the MLE, and a smoothed MLE for the interval censoring case 2 problem, focusing on their asymptotic properties.

Findings

The estimators' asymptotic distributions are characterized.

Simulation results compare estimator performance.

Smoothed MLE shows improved accuracy in certain scenarios.

Abstract

We study three estimators for the interval censoring case 2 problem, a histogram-type estimator, proposed in Birg\'e (1999), the maximum likelihood estimator (MLE) and the smoothed MLE, using a smoothing kernel. Our focus is on the asymptotic distribution of the estimators at a fixed point. The estimators are compared in a simulation study.