A note on the generalized maximum likelihood estimator in partial Koziol-Green model

The proportional hazards model with partially informative censoring has been studied by Gather and Pawlitschko [1998. Metrika 48, 189-207] and their partial Abdushukurov-Cheng-Lin (PACL) estimator is a nonparametric estimator of the underlying survival function of the model. Zhang and Rao [2004. Metrika 59, 125-136] have derived the generalized maximum likelihood estimator of the underlying survival function using Kiefer-Wolfowitz theory. In this note, we show that these two estimators are asymptotically equivalent.