The $\mathrm{\infty }$-S test via regression quantile affine LASSO

A novel test in the linear ${\mathrm{\ell }}_1$ (LAD) and quantile regressions is proposed, based on the scores provided by the dual variables (signs) arising in the calculation of the (so-called) affine-lasso estimate–a Rao-type, Lagrange multiplier test using the thresholding, towards the null hypothesis of the test, function of the latter estimate.