Prediction from randomly right censored data

Let X be a random vector taking values in IR d , let Y be a bounded random variable, and let C be a right censoring random variable operating on Y. It is assumed that C is independent of (X; Y), the distribution function of C is continuous and the support of the distribution of Y is a proper subset of the support of the distribution of C. Given a sample fX i ; minfY i ; C i g; I Y i C i ] g and a vector of covariates X, we want to construct an estimate of Y such that the mean squared error is minimized. Without censoring, i.e. for C = 1 almost surely, it is well{known that the mean squared error of suitably deened kernel, partitioning, nearest neighbor, least squares and smoothing spline estimates converges for every distribution of (X; Y) to the optimal value almost surely, if the sample size tends to innnity. In this paper, we modify the above estimates and show that in the right random censoring model described above the same is true for the modiied estimates.