Dimension reduction in the presence of censored data.

Summary We consider regression models where the explained variable is right-censored randomly. We propose new estimators of the regression function in parametric models, and we propose a non-parametric test of fit to these models. We extend these methods to the study of the semi-parametric "single-index" model, generalizing dimension reduction techniques used in the absence of censoring. We first consider models with stronger identifiability assumptions, before working in a framework where the explained variable and the censoring are conditionally independent of the explanatory variables. We develop a new dimension reduction approach for this type of problem.