Bootstrap Methods for Testing Asymptotic Dependence in Multivariate Heavy-Tailed Data

Bootstrap Methods for Testing Asymptotic Dependence in Multivariate Heavy-Tailed Data | 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 Bootstrap Methods for Testing Asymptotic Dependence in Multivariate Heavy-Tailed Data Tiandong Wang, Sidney Resnick This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7360860/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 7 You are reading this latest preprint version Abstract The ability to unambiguously classify the asymptotic dependence structure of multivariate data is often beyond the capability of graphical, exploratory tools. We present a rigorous and practical classification framework that leads to categorizing dependence structures into four main cases: (i) asymptotic independence, (ii) strong dependence, (iii) full dependence, and (iv) weak dependence. For bivariate non-negative heavy tailed data, switch to polar coordinates with the L 1 norm and these four cases are characterized respectively by the concentration of the limit angular measure on (i) {0, 1}, (ii) a proper subset of [0, 1], (iii) a single point, and (iv) the whole interval [0, 1]. Based on bootstrap methods we arrive at a comprehensive and theoretically justified classification tool. Here we demonstrate this tool using simulated data as well as the Finnish rainfall data. Bootstrap multivariate regular variation asymptotic dependence extremal dependence Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 30 Mar, 2026 Reviews received at journal 06 Feb, 2026 Reviewers agreed at journal 07 Nov, 2025 Reviewers invited by journal 07 Nov, 2025 Editor assigned by journal 14 Aug, 2025 Submission checks completed at journal 14 Aug, 2025 First submitted to journal 13 Aug, 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. 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-7360860","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":541658263,"identity":"62f196e4-cba8-494f-af02-3960eb1514c0","order_by":0,"name":"Tiandong Wang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4UlEQVRIiWNgGAWjYFCCBDApx97AYABiMDYQ0sAD1WLMc4BULYk9RGuxZ09gk/i5oza9RyJ54+cCBhvZDQeYnz3AawvPAzbJ3jPHc3sk0oqlZzCkGW84wGZugFeLRALbDd62Y7n7JXIMpHkYDiduOMDDJkFIy82/bcfSeSRyjH/zMPwnTstt3raaBKAWM6AtB4jQcuYB+2/ZtgOGPTzPyqx5DJKNZx5mM8Orhb09gdnwbVudPA978ubbPBV2sn3Hm5/h1cLAwP8BSByGckBBxYxfPQzUEadsFIyCUTAKRiYAAD0yRB2ZxmlTAAAAAElFTkSuQmCC","orcid":"","institution":"Fudan University","correspondingAuthor":true,"prefix":"","firstName":"Tiandong","middleName":"","lastName":"Wang","suffix":""},{"id":541658264,"identity":"d10b7d09-e01b-49d5-a678-3725ad36305a","order_by":1,"name":"Sidney Resnick","email":"","orcid":"","institution":"Cornell University","correspondingAuthor":false,"prefix":"","firstName":"Sidney","middleName":"","lastName":"Resnick","suffix":""}],"badges":[],"createdAt":"2025-08-13 05:08:18","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7360860/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7360860/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":96145317,"identity":"b4929d80-2072-4733-a0fd-1056f1e1f3c8","added_by":"auto","created_at":"2025-11-18 06:30:47","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":3474,"visible":true,"origin":"","legend":"","description":"","filename":"36060efb39cc4ddc939c83ebf827d13d.json","url":"https://assets-eu.researchsquare.com/files/rs-7360860/v1/4c8138a4081d51137e304139.json"},{"id":96251599,"identity":"02dd9feb-6541-4951-acf4-15c8033cf462","added_by":"auto","created_at":"2025-11-19 07:39:50","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":815247,"visible":true,"origin":"","legend":"","description":"","filename":"ExtremesSubmission.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7360860/v1_covered_31cb3bf1-68bd-48e3-bbe5-4d354e1d8cea.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Bootstrap Methods for Testing Asymptotic Dependence in Multivariate Heavy-Tailed Data","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":"extremes","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"extr","sideBox":"Learn more about [Extremes](http://link.springer.com/journal/10687)","snPcode":"10687","submissionUrl":"https://submission.nature.com/new-submission/10687/3","title":"Extremes","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Bootstrap, multivariate regular variation, asymptotic dependence, extremal dependence","lastPublishedDoi":"10.21203/rs.3.rs-7360860/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7360860/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The ability to unambiguously classify the asymptotic dependence structure of multivariate data is often beyond the capability of graphical, exploratory tools. 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