On the Estimation of the Joint Distribution in Regression Models with Censored Responses

In a regression model with univariate censored responses, a new estimatorof the joint distribution function of the covariates and response is proposed,under the assumption that the response and the censoring variable are independentconditionally to the covariates. This estimator is an extension of themultivariate empirical function used in the uncensored case. Furthermore,under some simple additional identiability assumption, this estimator is notsensible to the "curse of dimensionality", so that it allows to infer on modelswith multidimensional covariates. Integrals with respect to this empiricalmeasure are considered. Consistency and asymptotic normality of these integralsover a class of functions is obtained, by deriving asymptotic i.i.d.representations. Several applications of the new estimator are proposed.