Relative density estimation with censored data

Abstract

Well-described tools for comparing two populations via their cumulative distribution functions are the so-called relative distribution R(t) = F { F-0(-1)(t)} and the corresponding relative density (or grade density) r(t). The authors propose a kernel-type estimator for the relative density r (t) in the situation where independent samples of right-censored observations are available from the two populations. It is shown that the estimator admits an asymptotic: representation from which its limit distribution can be obtained. The results generalize those of Cwik & Mielniczuk: (1993) in the complete sample case.