The kernel estimator is a widely used tool for the estimation of a density function. In this paper its adaptation to censored data using the Kaplan-Meier estimator is considered. Asymptotic properties of four estimators, arising naturally as a result of considering various types of bandwidths, are investigated. In particular we show that (i) both proposed estimators stemming from the nearest neighbor estimator have censoring-free variances and (ii) one of them is pointwise mean consistent.
"Some Asymptotic Properties of Kernel Estimators of a Density Function in Case of Censored Data." Ann. Statist. 14 (2) 766 - 773, June, 1986. https://doi.org/10.1214/aos/1176349954