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

TL;DR

This paper introduces a new statistical test for linear regression models based on affine-LASSO estimates, utilizing dual variables to perform Rao-type Lagrange multiplier testing for hypothesis evaluation.

Contribution

It proposes a novel $ abla$-S test leveraging affine-LASSO dual variables, enhancing hypothesis testing in linear $ au$-regression models.

Findings

The test effectively detects deviations from the null hypothesis.

It provides a Rao-type Lagrange multiplier framework for affine-LASSO.

The method is applicable to LAD and quantile regressions.

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.