The copula-graphic estimator in censored nonparametric location-scale regression models

A common assumption when working with randomly right censored data, is the independence between the variable of interest Y (the survival time) and the censoring variable C. This assumption, which is not testable, is however unrealistic in certain situations. Let us assume that for a given covariate X, the dependence between the variables Y and C is described via a known copula. Additionally assume that Y is the response variable of a heteroscedastic regression model Y=m(X)+σ(X)ɛ, where the error term ε is independent of the explanatory variable X, and the functions m and σ are ‘smooth’. An estimator of the conditional distribution of Y given X under this model is then proposed, and the asymptotic normality of this estimator is shown. The small sample performance of the estimator is also studied, and the advantages/drawbacks of this estimator with respect to competing estimators are discussed