Kernel density estimation based on progressive type-II censoring

Progressive censoring is essential for researchers in industry as a mean to remove subjects before the final termination point in order to save time and reduce cost. Recently, kernel density estimation has been intensively investigated due to its asymptotic properties and applications. In this paper, we investigate the asymptotic properties of the kernel density estimators based on progressive type-II censoring and their application to hazard function estimation. A bias-adjusted kernel density estimator is also proposed. Our simulation indicates that the kernel density estimates under progressive type-II censoring is competitive compared with kernel density estimates under simple random sampling, depending on the censoring schemes. An example regarding failure times of aircraft windshields is used to illustrate the proposed methods.