Location estimation in nonparametric regression with censored data

Consider the heteroscedastic model Y = m ( X ) + σ ( X ) ɛ , where ɛ and X are independent, Y is subject to right censoring, m ( · ) is an unknown but smooth location function (like e.g. conditional mean, median, trimmed mean … ) and σ ( · ) an unknown but smooth scale function. In this paper we consider the estimation of m ( · ) 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 ( · ) , which cannot be estimated consistently in a completely nonparametric way, whenever high quantiles of the conditional distribution of Y given X = x are involved. ain the asymptotic properties of the proposed estimator of m ( x ) and study its finite sample behaviour in a simulation study. The method is also applied to a study of quasars in astronomy.