Estimation of a distribution under generalized censoring

Abstract

a b s t r a c tThis paper focuses on the problem of the estimation of a distribution on an arbitrary complete separable metric space when the data points are subject to censoring by a general class of random sets. If the censoring mechanism is either totally observable or totally ordered, a reverse probability estimator may be defined in this very general framework. Functional central limit theorems are proven for the estimator when the underlying space is Euclidean. Applications are discussed, and the validity of bootstrap methods is established in each case.