Semiparametric estimation of a partially linear censored regression model

In this paper we propose an estimation procedure for a censored regression model where the latent regression function has a partially linear form. Based on a conditional quantile restriction, we estimate the model by a two stage procedure. The first stage nonparametrically estimates the conditional quantile function at in-sample and appropriate out-of-sample points, and the second stage involves a simple weighted least squares procedure. The proposed procedure is shown to have desirable asymptotic properties under regularity conditions that are standard in the literature. A small scale simulation study indicates that the estimator performs well in moderately sized samples.