Remire: Robust extremile regression in high dimensions

Remire: Robust extremile regression in high dimensions | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Remire: Robust extremile regression in high dimensions Weixi Sun, Shanshan Wang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5161987/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Unconditional extremiles offer significant advantages over quantiles in risk management, as they satisfy the coherency axioms and provide various interpretative benefits. However, the application of extremile regression in multivariate conditional settings remains underexplored. In this paper, we propose a (penalized) robust linear extremile regression model (remire), incorporating the Huber loss function in place of the squared loss to enhance robustness against heavy-tailed errors. For high-dimensional data, we introduce a variable selection method using a folded concave penalty, and design an iteratively reweighted l1-penalized procedure for estimation. Each iteration’s estimation is solved via a local adaptive majorize-minimization algorithm. The proposed method exhibits desirable properties and performs well in finite samples, as demonstrated through comprehensive numerical studies. We further illustrate its practical utility with a real data application focused on childhood malnutrition. Extremile regression Robustness Heavy-tailed error Folded concave penalty Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5161987","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":369275036,"identity":"cd8105f3-6e59-4676-b719-6b6f05cc6658","order_by":0,"name":"Weixi Sun","email":"","orcid":"","institution":"Beihang University","correspondingAuthor":false,"prefix":"","firstName":"Weixi","middleName":"","lastName":"Sun","suffix":""},{"id":369275037,"identity":"7ff5200b-6ef1-45ae-b64e-28a43f7926a1","order_by":1,"name":"Shanshan Wang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzElEQVRIiWNgGAWjYPACmwQIzUa8ljTStRwmQYt8/xnDzwW/zucZHD/8gOFD2WEG/tkN+LUY3Mgxlp7Zd7vY4EyaAeOMc4cZJO4cIKBFgneDNG/P7cQNBxIMmHnbDgNFEgg57Ozm37w95xI3nH/+gfkvMVoYDuRuk+b5cSBxw40cA2ZGYrQY3Mj/Zs3bkFwseeNNwcGec+k8EjcIOuxY8m2eP3Z5fOfTNz74UWYtxz+DkMNAgLEN6kgg5iFCPQj8IVLdKBgFo2AUjEwAALP6SGnm8hrjAAAAAElFTkSuQmCC","orcid":"","institution":"Beihang University","correspondingAuthor":true,"prefix":"","firstName":"Shanshan","middleName":"","lastName":"Wang","suffix":""}],"badges":[],"createdAt":"2024-09-27 03:38:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5161987/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5161987/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":67345264,"identity":"3e0a008c-593f-406f-9491-94d02636fdeb","added_by":"auto","created_at":"2024-10-24 02:21:01","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":604702,"visible":true,"origin":"","legend":"","description":"","filename":"Remire.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5161987/v1_covered_cc5f768a-d8f1-4a6e-bb68-22cd31c811ec.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Remire: Robust extremile regression in high dimensions","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Extremile regression, Robustness, Heavy-tailed error, Folded concave penalty","lastPublishedDoi":"10.21203/rs.3.rs-5161987/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5161987/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eUnconditional extremiles offer significant advantages over quantiles in risk management, as they satisfy the coherency axioms and provide various interpretative benefits. However, the application of extremile regression in multivariate conditional settings remains underexplored. In this paper, we propose a (penalized) robust linear extremile regression model (remire), incorporating the Huber loss function in place of the squared loss to enhance robustness against heavy-tailed errors. For high-dimensional data, we introduce a variable selection method using a folded concave penalty, and design an iteratively reweighted l1-penalized procedure for estimation. Each iteration’s estimation is solved via a local adaptive majorize-minimization algorithm. The proposed method exhibits desirable properties and performs well in finite samples, as demonstrated through comprehensive numerical studies. We further illustrate its practical utility with a real data application focused on childhood malnutrition.\u003c/p\u003e","manuscriptTitle":"Remire: Robust extremile regression in high dimensions","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-10-24 02:12:53","doi":"10.21203/rs.3.rs-5161987/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"0701791b-a747-4bdd-87a8-75ccedd41ebc","owner":[],"postedDate":"October 24th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-10-24T02:12:53+00:00","versionOfRecord":[],"versionCreatedAt":"2024-10-24 02:12:53","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5161987","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5161987","identity":"rs-5161987","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}