Non parametric multivariate distribution estimation under right censoring

A non parametric estimator of the joint distribution function of a positive bivariate random vector is introduced. The case where one of the two variables is subject to right censoring is considered. To construct the proposed estimator, Poisson distributions are used for smoothing the empirical estimator of Stute (1993). The strong uniform convergence is established. Also, by stating the asymptotic i.i.d. representation, the asymptotic bias, variance, and normality are deduced. The smooth estimator is applied for analyzing survival data from patients with advanced lung cancer.