Practical confidence intervals for regression quantiles

Routine applications of quantile regression analysis require reliable and practical algorithms for estimating standard errors, variance-covariance matrices, as well as confidence intervals. Because the asymptotic variance of a quantile estimator depends on error densities, some standard large-sample approximations have been found to be highly sensitive to minor deviations from the iid error assumption. In this article we propose a time-saving resampling method based on a simple but useful modification of the Markov chain marginal bootstrap (MCMB) to construct confidence intervals in quantile regression. This method is compared to several existing methods with favorable performance in speed, accuracy, and reliability. We also make practical recommendations based on the quantreg package contributed by Roger Koenker and a new package rqmcmb2 developed by the first two authors. These recommendations also apply to users of the new SAS procedure PROC QUANTREG, available from Version 9.2 of SAS.