We show that regression quantiles, which could be computed as solutions of a linear programming problem, and the solutions of the corresponding dual problem, which we call the regression rank-scores, generalize the duality of order statistics and of ranks from the location to the linear model. Noting this fact, we study the regression quantile and regression rank-score processes in the heteroscedastic linear regression model, obtaining some new estimators and interesting comparisons with existing estimators.
"Regression Rank Scores and Regression Quantiles." Ann. Statist. 20 (1) 305 - 330, March, 1992. https://doi.org/10.1214/aos/1176348524