4.9 Let us consider an R-estimator minimizing the rank dispersion (4.48)

If we set = then this R-estimator coincides with the slope components of regression -quantile b () solving (4.54), see Jurecková (2017) and Jurecková
et. al. (2017).
For arbitrary fixed = , compute and compare both estimates (the R-estimator and the slope components of b ()) for the Engel food expenditure data (dataset engel in package quantreg) and for the stackloss dataset from Example 4.4. For the computation of the R-estimate with the specified scores you can use the function rfit0 and for the rank dispersion criterion of the estimators the function disp0. Both functions can be found in Appendix A.

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with the scores an (i) = ri/n = n (-1)/n (u)du, where 4x(u) = - I[u