Single index regression models in the presence of censoring depending on the covariates

Consider a random vector (X ′, Y )′, where X is d-dimensional and Y is onedimensional. 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 single index model, and propose a new estimator of the parameters in this model. The asymptotic properties of all proposed estimators are obtained.