Density-estimation under the Koziol-Green model of censoring by penalized likelihood methods

Abstract

We propose two density estimators of the survival distribution in the setting of the Koziol-Green random-censoring model. The estimators are obtained by maximum-penalized-likelihood methods, and we provide an algorithm for their numerical evaluation. We establish the strong consistency of the estimators in the Hellinger metric, the L(p)-norms, p = 1,2,-infinity, and a Sobolev norm, under mild conditions on the underlying survival density and the censoring distribution.