This paper is concerned with the nonparametric estimation of regression quantiles of a response variable that is randomly censored. Using results on the strong uniform convergence rate of U-processes, we derive a global Bahadur representation for a class of locally weighted polynomial estimators, which is sufficiently accurate for many further theoretical analyses including inference. Implications of our results are demonstrated through the study of the asymptotic properties of the average derivative estimator of the average gradient vector and the estimator of the component functions in censored additive quantile regression models.
Centre for microdata methods and practice