NPMLE based on coarse data in $\sigma$-VC Helly classes
Abstract
We consider nonparametric maximum likelihood estimators of a probability
measure based on coarse data. Coarsening is a general model of incomplete
data which includes grouping and censoring with measurable sets. Asymptotic
consistency of nonparametric maximum likelihood estimators is established
under nearly sharp conditions in several modes of convergence. The results
cover the Turnbull (1976) set-censoring model and certain multivariate
extensions of it. The proofs are based on a likelihood ratio inequality for
additive set functions in a field against measures, and on certain
characterizations of the nonparametric maximum likelihood estimators.
R E F R E S H M E N T S
4:00 To 4:25 PM
Kenneth W. Anderson
Memorial Reading Room
