{"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/penalized-maximum-tangent-likelihood","title":"Penalized Maximum Tangent Likelihood Estimation and Robust Variable Selection","arxiv_id":"1708.05439","date":"2017-08-17","proceeding":null,"authors":["Yichen Qin","Shaobo Li","Yang Li","Yan Yu"],"abstract":"We introduce a new class of mean regression estimators -- penalized maximum tangent likelihood estimation -- for high-dimensional regression estimation and variable selection. We first explain the motivations for the key ingredient, maximum tangent likelihood estimation (MTE), and establish its asymptotic properties. We further propose a penalized MTE for variable selection and show that it is $\\sqrt{n}$-consistent, enjoys the oracle property. The proposed class of estimators consists penalized $\\ell_2$ distance, penalized exponential squared loss, penalized least trimmed square and penalized least square as special cases and can be regarded as a mixture of minimum Kullback-Leibler distance estimation and minimum $\\ell_2$ distance estimation. Furthermore, we consider the proposed class of estimators under the high-dimensional setting when the number of variables $d$ can grow exponentially with the sample size $n$, and show that the entire class of estimators (including the aforementioned special cases) can achieve the optimal rate of convergence in the order of $\\sqrt{\\ln(d)/n}$. Finally, simulation studies and real data analysis demonstrate the advantages of the penalized MTE.","url_abs":"http://arxiv.org/abs/1708.05439v2","url_pdf":"http://arxiv.org/pdf/1708.05439v2.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":"penalized-maximum-tangent-likelihood","repo_url":"https://github.com/cran/MTE","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"penalized-maximum-tangent-likelihood","repo_url":"https://github.com/shaobo-li/MTE","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}