  Consider a random vector (X',Y)', where X is d-dimensional and Y is
one-dimensional. We assume that Y is subject to random right censoring. The aim
of this paper is twofold. First, we propose a new estimator of the joint
distribution of (X',Y)'. This estimator overcomes the common
curse-of-dimensionality problem, by using a new dimension reduction technique.
Second, we assume that the relation between X and Y is given by a mean
regression single index model, and propose a new estimator of the parameters in
this model. The asymptotic properties of all proposed estimators are obtained.
