On the Asymptotic Properties of a Kernel-Type Quantile Estimator from Censored Samples.

In reliability and medical studies, it is often of interest to estimate various quantiles of the unknown lifetime distribution. In particular, the median lifetime and extreme quantiles are of interest to the experimenter in such studies. In many life testing and medical follow-up experiments, however, arbritrarily right-censored data arise, and it is important to be able to estimate the quantiles of interest based on the censored data. For such data, some kernel-type quantile estimators are considered in this paper which give smoother estimates than the usual product-limit quantile function. Keywords Random right-censorship Kernel estimation Product-limit quantile function Asymptotic normality and Mean-square convergence.