Penalized robust estimating equation and variable selection in a partially linear single-index varying-coefficient model

Penalized robust estimating equation and variable selection in a partially linear single-index varying-coefficient model | 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 Penalized robust estimating equation and variable selection in a partially linear single-index varying-coefficient model Gaorong Li, Liugen Xue, Riquan Zhang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6533938/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 25 Oct, 2025 Read the published version in Statistics and Computing → Version 1 posted 10 You are reading this latest preprint version Abstract This paper focuses on the variable selection and estimation for a partially linear single-index varying-coefficient model. A novel fusing L 1 and exponential integral penalty and a new loss function are proposed to construct the penalized robust estimating equation (PREE) for variable selection and estimations of the regression parameters. The consistency of the variable selection procedure and the oracle property of the regularized estimators are proved under some regularity conditions. The bias correction technique is employed in PREE to avoid undersmoothing of the coefficient functions. An iteration algorithm is proposed for estimating the regression parameters. The finite sample performance of our method is validated through simulation studies, and a real data analysis further confirms the validity of the proposed method. Fusing L1 and exponential integral Loss function Oracle property Partially linear single-index varying-coefficient model Penalized robust estimating equation Full Text Additional Declarations No competing interests reported. Supplementary Files SupplementPLSIVCMHDD.pdf Cite Share Download PDF Status: Published Journal Publication published 25 Oct, 2025 Read the published version in Statistics and Computing → Version 1 posted Editorial decision: Revision requested 28 Jul, 2025 Reviews received at journal 28 Jul, 2025 Reviews received at journal 10 Jun, 2025 Reviewers agreed at journal 05 May, 2025 Reviewers agreed at journal 05 May, 2025 Reviewers agreed at journal 05 May, 2025 Reviewers invited by journal 05 May, 2025 Editor assigned by journal 29 Apr, 2025 Submission checks completed at journal 29 Apr, 2025 First submitted to journal 26 Apr, 2025 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. 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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-6533938","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":453493303,"identity":"0976b11b-178f-4282-9ea0-2b78d23a6587","order_by":0,"name":"Gaorong Li","email":"","orcid":"","institution":"Beijing Normal University","correspondingAuthor":false,"prefix":"","firstName":"Gaorong","middleName":"","lastName":"Li","suffix":""},{"id":453493304,"identity":"b585a574-094c-42ea-99ed-1f85c98f29d4","order_by":1,"name":"Liugen Xue","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAxklEQVRIiWNgGAWjYBACPjBZcYAZTPMQo4UNTJ4BamEjSQtj2wEGErTwrzGT+DjvDrvB/QbGB2/bGOTNCWqReJYmOXPbM2aDYwzMhnPbGAx3NhDUcviYNO+2wyAtbNK8bQwJBgcIajnYJv13DlgL+2/itPA3H5NmbIDYwkykLWzJlj3HnjFLHktslpxzTsJwAyEt/PxnDG/8qLmTzHf48MEPb8ps5AnawiCRAKaSgbHTAOISUg+yBmKoHRFKR8EoGAWjYKQCAL/rPDz10m9aAAAAAElFTkSuQmCC","orcid":"","institution":"Henan University","correspondingAuthor":true,"prefix":"","firstName":"Liugen","middleName":"","lastName":"Xue","suffix":""},{"id":453493305,"identity":"21eb3f41-c724-43d4-b049-91461f5f2fe1","order_by":2,"name":"Riquan Zhang","email":"","orcid":"","institution":"Shanghai University of International Business and Economics","correspondingAuthor":false,"prefix":"","firstName":"Riquan","middleName":"","lastName":"Zhang","suffix":""}],"badges":[],"createdAt":"2025-04-26 09:08:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6533938/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6533938/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11222-025-10754-z","type":"published","date":"2025-10-25T16:16:12+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":94490297,"identity":"b0b02e6b-3505-4a82-a1ae-b0a6e3e41d27","added_by":"auto","created_at":"2025-10-27 17:08:56","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":493632,"visible":true,"origin":"","legend":"","description":"","filename":"PLSIVCMHDD.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6533938/v1_covered_d079b9fa-c080-4bb3-a12c-92977eb14154.pdf"},{"id":82324261,"identity":"9964400f-be61-46a1-89b2-0557f0858c44","added_by":"auto","created_at":"2025-05-09 06:00:29","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":131225,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementPLSIVCMHDD.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6533938/v1/7be635802ab9dbc566004a12.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Penalized robust estimating equation and variable selection in a partially linear single-index varying-coefficient model","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"statistics-and-computing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"stco","sideBox":"Learn more about [Statistics and Computing](http://link.springer.com/journal/11222)","snPcode":"11222","submissionUrl":"https://submission.nature.com/new-submission/11222/3","title":"Statistics and Computing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Fusing L1 and exponential integral, Loss function, Oracle property, Partially linear single-index varying-coefficient model, Penalized robust estimating equation","lastPublishedDoi":"10.21203/rs.3.rs-6533938/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6533938/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper focuses on the variable selection and estimation for a partially linear single-index varying-coefficient model. 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