Global Bahadur Representation For NonParametric Censored Regression Quantiles and its Applications

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.