Maximum smoothed likelihood estimators for the interval censoring model

TL;DR

This paper introduces the maximum smoothed likelihood estimator (MSLE) for interval censoring case 2, demonstrating its strong consistency, faster convergence rate, and normal limit distribution compared to the traditional MLE.

Contribution

The paper provides a novel analysis of MSLE for interval censoring, including characterizations, consistency proofs, and convergence rate improvements over MLE.

Findings

MSLE is strongly consistent.

Convergence rate is $n^{-2/5}$ under smoothness conditions.

Limit distribution of MSLE is normal.

Abstract

We study the maximum smoothed likelihood estimator (MSLE) for interval censoring, case 2, in the so-called separated case. Characterizations in terms of convex duality conditions are given and strong consistency is proved. Moreover, we show that, under smoothness conditions on the underlying distributions and using the usual bandwidth choice in density estimation, the local convergence rate is $n^{-2/5}$ and the limit distribution is normal, in contrast with the rate $n^{-1/3}$ of the ordinary maximum likelihood estimator.