A consistency result in general censoring models

In this paper we prove a consistency result for sieved maximum likelihood estimators of the density in general random censoring models with covariates. The proof is based on the method of functional estimation. The estimation error is decomposed in a deterministic approximation error and the stochastic estimation error. The main part of the proof is to establish a uniform law of large numbers for the conditional log-likelihood functional, by using results and techniques from empirical process theory.