{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:42:19Z","timestamp":1760035339685,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,7,4]],"date-time":"2025-07-04T00:00:00Z","timestamp":1751587200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key Research and Development Program of China","award":["2021YFA1000102","ZR2024MA074","24YJA910003","23CX03012A"],"award-info":[{"award-number":["2021YFA1000102","ZR2024MA074","24YJA910003","23CX03012A"]}]},{"name":"Natural Science Foundation (NSF) project of Shandong Province of China","award":["2021YFA1000102","ZR2024MA074","24YJA910003","23CX03012A"],"award-info":[{"award-number":["2021YFA1000102","ZR2024MA074","24YJA910003","23CX03012A"]}]},{"name":"Ministry of education of Humanities and Social Science project","award":["2021YFA1000102","ZR2024MA074","24YJA910003","23CX03012A"],"award-info":[{"award-number":["2021YFA1000102","ZR2024MA074","24YJA910003","23CX03012A"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["2021YFA1000102","ZR2024MA074","24YJA910003","23CX03012A"],"award-info":[{"award-number":["2021YFA1000102","ZR2024MA074","24YJA910003","23CX03012A"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper proposes a robust variable selection method that incorporates prior information through linear constraints. For more than a decade, penalized likelihood frameworks have been the predominant approach for variable selection, where appropriate loss and penalty functions are selected to formulate unconstrained optimization problems. However, in many specific applications, some prior information can be obtained. In this paper, we reformulate variable selection by incorporating prior knowledge as linear constraints. In addition, the loss function adopted in this paper is a robust exponential squared loss function, which ensures that the estimation of model parameter coefficient will not have a great impact when there are a few outliers in the dataset. This paper uses the designed solution algorithm to calculate the estimated values of coefficients and some other parameters, and finally conducts numerical simulations and a real-data experiment. Experimental results demonstrate that our model significantly improves estimation robustness compared to existing methods, even in outlier-contaminated scenarios.<\/jats:p>","DOI":"10.3390\/axioms14070516","type":"journal-article","created":{"date-parts":[[2025,7,7]],"date-time":"2025-07-07T06:03:13Z","timestamp":1751868193000},"page":"516","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Exponential Squared Loss-Based Robust Variable Selection with Prior Information in Linear Regression Models"],"prefix":"10.3390","volume":"14","author":[{"given":"Hejun","family":"Wei","sequence":"first","affiliation":[{"name":"College of Science, China University of Petroleum, Qingdao 266580, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tian","family":"Jin","sequence":"additional","affiliation":[{"name":"College of Science, China University of Petroleum, Qingdao 266580, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yunquan","family":"Song","sequence":"additional","affiliation":[{"name":"College of Science, China University of Petroleum, Qingdao 266580, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,4]]},"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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