Direct use of the empirical quantile function provides a standard distribution-free approach to constructing confidence intervals and confidence bands for population quantiles. We apply this method to construct confidence intervals and confidence bands for regression quantiles and to construct prediction intervals based on sample regression quantiles. Comparison of the direct method with the studentization and the bootstrap methods are discussed. Simulation results show that the direct method has the advantage of robustness against departure from the normality assumption of the error terms.
"Direct use of regression quantiles to construct confidence sets in linear models." Ann. Statist. 24 (1) 287 - 306, February 1996. https://doi.org/10.1214/aos/1033066210