Goodness-of-fit, correlation tests, Cramér-von Mises, empirical and quantile/processes, Kolmogorov-Smirnov, Shapiro-Wilk, strong approximations, Wasserstein distance, Primary 62F05, 62E20, secondary 60F25,

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Nonextreme regression quantiles are estimated nonparametrically on the basis of local polynomial approximations to the true conditional quantile function. The consistency of the estimator is shown.The asymptotic normality is proven and the asymptotic confidence interval for the regression quantile is constructed.

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