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

Sylvain Sardy; Ivan Mizera; Xiaoyu Ma; Hugo Gaible

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

Methodology 2025-12-23 v3

Authors: Sylvain Sardy , Ivan Mizera , Xiaoyu Ma , Hugo Gaible

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.

Cite

@article{arxiv.2409.04256,
  title  = {The $\infty$-S test via regression quantile affine LASSO},
  author = {Sylvain Sardy and Ivan Mizera and Xiaoyu Ma and Hugo Gaible},
  journal= {arXiv preprint arXiv:2409.04256},
  year   = {2025}
}

Comments

18 pages, 4 figures

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