Nonparametric (smoothed) likelihood and integral equations

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.

arXiv comment12 figures, invited paper with discussion for the Journal of Statistical Planning and Inference