Online Updated Learning for Extremiles via Parametric Quantile Estimation

Online Updated Learning for Extremiles via Parametric Quantile Estimation | 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 Online Updated Learning for Extremiles via Parametric Quantile Estimation Jia-Yuan Liang, Rong Jiang, Xin-Yi Wang, Yan-Bin Zhao This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7971795/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract Extremile, a recently introduced coherent risk measure, has demonstrated significant potential as a valuable tool in financial and actuarial applications. However, developing a real time estimator for Extremile in streaming data environments presents substantial computational challenges. These difficulties primarily stem from the inability to generate ordered samples in data streams characterized by single-pass processing and undefined terminal size. To overcome this limitation, we propose an efficient online updating algorithm for Extremile based on a parameterized quantile-based approach by using generalized lambda distribution. Theoretically, this methodology eliminates the need for repeated full dataset reprocessing while maintaining asymptotic property. Both simulation studies and real data analyses are conducted to evaluate the finite sample performance of the proposed methods. extremile streaming data online updated learning generalized lambda distribution composite quantile regression Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 08 Feb, 2026 Reviews received at journal 08 Feb, 2026 Reviews received at journal 10 Jan, 2026 Reviewers agreed at journal 27 Nov, 2025 Reviewers agreed at journal 25 Nov, 2025 Reviewers invited by journal 04 Nov, 2025 Editor assigned by journal 30 Oct, 2025 Submission checks completed at journal 29 Oct, 2025 First submitted to journal 28 Oct, 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. We do this by developing innovative software and high quality services for the global research community. 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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-7971795","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":539950584,"identity":"8943279f-d359-4d2e-bbcf-333d494ae8cd","order_by":0,"name":"Jia-Yuan Liang","email":"","orcid":"","institution":"Donghua University","correspondingAuthor":false,"prefix":"","firstName":"Jia-Yuan","middleName":"","lastName":"Liang","suffix":""},{"id":539950585,"identity":"ac5e2cb3-27dc-4f61-bb91-dc7f639a7700","order_by":1,"name":"Rong Jiang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9UlEQVRIiWNgGAWjYBACxmYYi72BgSGxAcRKIFYLzwEitSCABFAlIzFamNuZnz38uscmTz7y+TOJhztsGPjZcwwYfu7A5zA2c2OZZ2nFhrdzzCQSz6QxSPa8MWDsPYNPC4OZtMSBw4kbZ+ewSSS2HWYwuJFjwMzYhk8L+zeIlpnHnwG1/GewJ6yFx0zyA1DLfAkGoMPaDjAYSBDWUibNcCAtcQNPjrFF4plkHokzzwoO9uLRYth/fJvkjwM2ifPbjz+8+XOHnRx/e/LGBz/xaWkABjQPkGFwACIAYjMcwK2BgUEe5LgfIEYDPmWjYBSMglEwogEAvJxSVDVfkf8AAAAASUVORK5CYII=","orcid":"","institution":"Shanghai University of International Business and Economics","correspondingAuthor":true,"prefix":"","firstName":"Rong","middleName":"","lastName":"Jiang","suffix":""},{"id":539950586,"identity":"56713ede-d789-45af-887b-a8835c640737","order_by":2,"name":"Xin-Yi Wang","email":"","orcid":"","institution":"Donghua University","correspondingAuthor":false,"prefix":"","firstName":"Xin-Yi","middleName":"","lastName":"Wang","suffix":""},{"id":539950588,"identity":"514bf942-c14c-493b-9476-b08ef9c1d410","order_by":3,"name":"Yan-Bin Zhao","email":"","orcid":"","institution":"Shanghai Polytechnic University","correspondingAuthor":false,"prefix":"","firstName":"Yan-Bin","middleName":"","lastName":"Zhao","suffix":""}],"badges":[],"createdAt":"2025-10-28 17:20:56","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7971795/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7971795/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":95938847,"identity":"c07c92e5-7658-4f71-b362-5ae9a151d8f3","added_by":"auto","created_at":"2025-11-14 16:05:00","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":5222,"visible":true,"origin":"","legend":"","description":"","filename":"3954ca14622540cbb262126e902cd57b.json","url":"https://assets-eu.researchsquare.com/files/rs-7971795/v1/d37680dce4f56aea89b77076.json"},{"id":96245522,"identity":"5204e4a9-13c2-46b0-95aa-02d9e7e400f0","added_by":"auto","created_at":"2025-11-19 07:20:50","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":423277,"visible":true,"origin":"","legend":"","description":"","filename":"Onlineupdatedlearningforextremile.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7971795/v1_covered_c86c575d-6070-4832-9c5c-0331c303a7db.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Online Updated Learning for Extremiles via Parametric Quantile Estimation","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"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":"extremile, streaming data, online updated learning, generalized lambda distribution, composite quantile regression","lastPublishedDoi":"10.21203/rs.3.rs-7971795/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7971795/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Extremile, a recently introduced coherent risk measure, has demonstrated significant potential as a valuable tool in financial and actuarial applications. 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