Thresholding tests based on affine LASSO to achieve non-asymptotic nominal level and high power under sparse and dense alternatives in high dimension

Sylvain Sardy, Jairo Diaz-Rodriguez and Caroline Giacobino

Computational Statistics & Data Analysis, 2022, vol. 173, issue C

Abstract: Thresholding estimators such as the existing square-root and LAD LASSO, and the new affine and GLM LASSO with new link functions, have the ability to set coefficients to zero. They will yield new pivotal statistics which enjoy high power under sparse or dense alternative hypotheses. Under a general formalism, thresholding tests not only recover existing tests such as Rao score test and Fisher nonparametric sign test, but also unveil new tests, for the global/omnibus hypothesis in high dimension in particular. Although pivotal, the new statistics do not have a known distribution, so the critical value of the test is calculated by straightforward Monte Carlo, which yields exact level and high power as illustrated on simulated data.

Keywords: Generalized linear model; LASSO; Pivotal statistic; Sparsity (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:173:y:2022:i:c:s0167947322000871

DOI: 10.1016/j.csda.2022.107507

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