Relative density estimation with censored data

Well described tools for comparing two populations via their cumulative distribution functions F and F0 are the so-called relative distribution R (t) = F { F−1 0 (t) } and the corresponding relative density (or grade density) r (t). The authors propose a kerneltype 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 Ćwik & Mielniczuk (1993) in the complete sample case.