Asymptotic normality of kernel estimators based upon incomplete data

摘要

In this paper, we are concerned with nonparametric estimation of the density and the failure rate functions of a random variable X which is at risk of being censored. First, we establish the asymptotic normality of a kernel density estimator in a general censoring setup. Then, we apply our result in order to derive the asymptotic normality of both the density and the failure rate estimators in the cases of right, twice and doubly censored data. Finally, the performance and the asymptotic Gaussian behaviour of the studied estimators, based on either doubly or twice censored data, are illustrated through a simulation study.