Location estimation in nonparametric regression with censored data

Consider the heteroscedastic model Y =m (X) +sigma(X)epsilon, where epsilon and X are independent, Y is subject to right censoring, m (center dot) is an unknown but smooth location function (like e.g. conditional mean, median, trimmed mean...) and sigma(center dot) an unknown but smooth scale function. In this paper we consider the estimation of m(center dot) under this model. The estimator we propose is a Nadaraya-Watson type estimator, for which the censored observations are replaced by 'synthetic' data points estimated under the above model. The estimator offers an alternative for the completely nonparametric estimator of m (center dot), which cannot be estimated consistently in a completely nonparametric way, whenever high quantiles of the conditional distribution of Y given X = x are involved. We obtain the asymptotic properties of the proposed estimator of m (x) and study its finite samplebehaviour in a simulation study. The method is also applied to a study of quasars in astronomy. (c) 2007 Elsevier Inc. All rights reserved.