The choice of a smoothing parameter or bandwidth is crucial when applying non- parametric regression estimators. In nonparametric mean regression various meth- ods for bandwidth selection exists. But in nonparametric quantile regression band- width choice is still an unsolved problem. In this...

Let {(Xi,Yi): 1 [less-than-or-equals, slant] i[less-than-or-equals, slant]n} be a sample of size n from a bivariate population, 0 p 1, and let [xi]p(x) be the p-quantile of Y1 given X1 = x. Estimation of [xi]p(x) when it is monotone in x for all 0 p 1, has been studied in the literature....