Estimation in nonparametric location-scale regression models with censored data

Consider the random vector (X; Y ), where X is completely observed and Y is subject to random right censoring. It is well known that the completely nonparametric kernel estimator of the conditional distribution F (.|x) of Y given X = x suffers from inconsistency problems in the right tail (Beran, 1981), and hence any location function m(x) that involves the right tail of F (.|x)(like the conditional mean) cannot be estimated consistently in a completely nonparametric way . In this paper we propose an alternative estimator of m(x), that, under certain conditions, does not share the above inconsistency problems. The estimator is constructed under the model Y = m(X) + σ(X)ε, where ε and X are independent and σ(.) is an unknown scale function. We obtain the asymptotic properties of the proposed estimator of m(x), we compare it with the completely nonparametric estimator via simulations and apply it to a study of quasars in astronomy