Nonparametric (smoothed) likelihood and integral equations

TL;DR

This paper explores the link between nonparametric smoothed likelihood estimators for inverse problems and integral equations, focusing on interval censoring and deconvolution, and discusses their asymptotic efficiency.

Contribution

It establishes a connection between nonparametric likelihood estimators and integral equations, providing new insights into their properties and efficiency in inverse problems.

Findings

Connection between likelihood estimators and integral equations

Application to interval censoring and deconvolution problems

Analysis of asymptotic efficiency of MLEs

Abstract

We show that there is an intimate connection between the theory of nonparametric (smoothed) maximum likelihood estimators for certain inverse problems and integral equations. This is illustrated by estimators for interval censoring and deconvolution problems. We also discuss the asymptotic efficiency of the MLE for smooth functionals in these models.