{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/the-ell-test-leveraging-sparsity-in-the","title":"The $\\ell$-test: leveraging sparsity in the Gaussian linear model for improved inference","arxiv_id":"2406.18390","date":"2024-06-26","proceeding":null,"authors":["Souhardya Sengupta","Lucas Janson"],"abstract":"We develop novel LASSO-based methods for coefficient testing and confidence interval construction in the Gaussian linear model with $n\\ge d$. Our methods' finite-sample validity is identical to that of their ubiquitous ordinary-least-squares-$t$-test-based analogues, yet have substantially higher power when the true coefficient vector is sparse. In particular, under sparsity our coefficient test, which we call the $\\ell$-test, performs like the \\emph{one-sided} $t$-test (despite not being given any information about the sign), and $\\ell$-test-based confidence intervals are correspondingly shorter than the standard $t$-test-based intervals. The nature of the $\\ell$-test directly provides a novel exact adjustment conditional on LASSO selection for post-selection inference, allowing for the construction of post-selection $p$-values and confidence intervals. None of our methods require resampling or Monte Carlo estimation. We perform a variety of simulations and a real data analysis on an HIV drug resistance data set to demonstrate the benefits of the $\\ell$-test. We additionally show that the $\\ell$-test can be applied to a large class of asymptotically Gaussian estimators, dramatically expanding its applicability beyond linear models.","url_abs":"https://arxiv.org/abs/2406.18390v1","url_pdf":"https://arxiv.org/pdf/2406.18390v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"the-ell-test-leveraging-sparsity-in-the","repo_url":"https://github.com/SSouhardya/l-test","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}