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

Abstract

A novel test in the linear ${\ell }_1$ (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.

18 pages, 4 figures