Estimation of a Nonparametric Censored Regression Model

In this paper we consider identiication and estimation of a censored nonparametric location scale model. We rst show that in the case where the location function is strictly less than the ((xed) censoring point for all values in the support of the explanatory variables, then the location function is not identiied anywhere. In contrast, if the location function is greater or equal to the censor-ing point with positive probability, then the location function is identiied on the entire support, including the region where the location function is below the censoring point. In the latter case we propose a simple estimation procedure based on combining conditional quantile estimators for three distinct quantiles. The new estimator is shown to converge at the optimal nonparametric rate with a limiting normal distribution. A small scale simulation study indicates that the proposed estimation procedure performs well in nite samples.