Density estimation under the koziol-green model of censoring by penalized likelihood methods

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, ∞, and a Sobolev norm, under mild conditions on the underlying survival density and the censoring distribution.