Density estimation in the simple proportional hazards model

In the simple proportional hazards model of random right censorship the limiting variance vACL2(x) at x of the kernel density estimator based on the Abdushukurov-Cheng-Lin estimator is shown to be equal to the corresponding variance pertaining to the Kaplan-Meier estimator times the expected proportion p of uncensored observations. More surprisingly, for appropriate p, vACL2(x) is smaller than the asymptotic variance of the classical kernel estimator based on a complete sample, for any x below the (1 - e-1)-quantile.