{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T07:15:56Z","timestamp":1761808556909,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,10,15]],"date-time":"2022-10-15T00:00:00Z","timestamp":1665792000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"S&amp;T Program of Hebei","award":["22557688D","HB22JMRH025","20220202086"],"award-info":[{"award-number":["22557688D","HB22JMRH025","20220202086"]}]},{"name":"Military and Civil integration in Hebei Province","award":["22557688D","HB22JMRH025","20220202086"],"award-info":[{"award-number":["22557688D","HB22JMRH025","20220202086"]}]},{"name":"Hebei Province social science development research project","award":["22557688D","HB22JMRH025","20220202086"],"award-info":[{"award-number":["22557688D","HB22JMRH025","20220202086"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Least absolute deviation is proposed as a robust estimator to solve the problem when the error has an asymmetric heavy-tailed distribution or outliers. In order to be insensitive to the above situation and select the truly important variables from a large number of predictors in the linear regression, this paper introduces a two-stage variable selection method named relaxed lad lasso, which enables the model to obtain robust sparse solutions in the presence of outliers or heavy-tailed errors by combining least absolute deviation with relaxed lasso. Compared with lasso, this method is not only immune to the rapid growth of noise variables but also maintains a better convergence rate, which is Opn\u22121\/2. In addition, we prove that the relaxed lad lasso estimator has the property of consistency at large samples; that is, the model selects the number of important variables with a high probability of convergence to one. Through the simulation and empirical results, we further verify the outstanding performance of relaxed lad lasso in terms of prediction accuracy and the correct selection of informative variables under the heavy-tailed distribution.<\/jats:p>","DOI":"10.3390\/sym14102161","type":"journal-article","created":{"date-parts":[[2022,10,17]],"date-time":"2022-10-17T05:08:02Z","timestamp":1665983282000},"page":"2161","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Robust Variable Selection Based on Relaxed Lad Lasso"],"prefix":"10.3390","volume":"14","author":[{"given":"Hongyu","family":"Li","sequence":"first","affiliation":[{"name":"The Graduate School, Woosuk University, Wanju-gun 55338, Korea"}]},{"given":"Xieting","family":"Xu","sequence":"additional","affiliation":[{"name":"College of Economics, Hebei GEO University, Shijiazhuang 050031, China"}]},{"given":"Yajun","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Business Administration, Chongqing Technology and Business University, Chongqing 400067, China"}]},{"given":"Xi","family":"Yu","sequence":"additional","affiliation":[{"name":"HBIS Supply Chain Management Co., Ltd., Shijiazhuang 050001, China"}]},{"given":"Tong","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Economics, Hebei GEO University, Shijiazhuang 050031, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5590-3109","authenticated-orcid":false,"given":"Rufei","family":"Zhang","sequence":"additional","affiliation":[{"name":"Hebei Center for Ecological and Environmental Geology Research, Hebei GEO University, Shijiazhuang 050031, China"},{"name":"Reaserch Center of Nutural Resources Assets, Hebei GEO University, Shijiazhuang 050031, China"},{"name":"Hebei Province Mineral Resources Development and Management and the Transformation and Upgrading of Resources Industry Soft Science Resrarch Base, Shijiazhuang 050031, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","article-title":"Regression shrinkage and selection via the lasso","volume":"58","author":"Tibshirani","year":"1996","journal-title":"J. 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