Complete f-moment convergence for arrays of rowwise mn-extended negatively dependent random variables and its application

Complete f-moment convergence for arrays of rowwise mn-extended negatively dependent random variables and its application | 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 Complete f -moment convergence for arrays of rowwise m n -extended negatively dependent random variables and its application Yanjiang Chen, Volodin Andrei, Xuejun Wang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9414003/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract As a key branch of probability theory and mathematical statistics, probability limit theory focuses on analyzing the convergence properties of random variable sequences and their associated distribution functions. Complete $f$-moment convergence is much general than complete convergence and complete moment convergence. In this paper, we study the complete $f$-moment convergence for rowwise $m_n$-extended negatively dependent random variables, which is a new dependence structure. The results on complete $f$-moment convergence are obtained under some suitable conditions, which generalize the corresponding ones in the literature. As an application, we establish the complete consistency for the G-M estimator of nonparametric regression models. Moreover, a series of simulations are implemented to show the numerical performance of theoretical results based on finite samples. MSC : 60F15; 62G20 rowwise mn-extended negatively dependent random variables complete fmoment convergence maximal weighted sums nonparametric regression models complete consistency Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 07 May, 2026 Reviewers agreed at journal 17 Apr, 2026 Reviewers agreed at journal 16 Apr, 2026 Reviewers invited by journal 15 Apr, 2026 Editor assigned by journal 14 Apr, 2026 Submission checks completed at journal 14 Apr, 2026 First submitted to journal 14 Apr, 2026 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-9414003","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":625072420,"identity":"020c30e1-c559-4377-8c02-130d2c65c47e","order_by":0,"name":"Yanjiang Chen","email":"","orcid":"","institution":"Anhui University","correspondingAuthor":false,"prefix":"","firstName":"Yanjiang","middleName":"","lastName":"Chen","suffix":""},{"id":625072421,"identity":"205b9afb-7477-4ede-b268-90c3e14bdc13","order_by":1,"name":"Volodin Andrei","email":"","orcid":"","institution":"University of Regina","correspondingAuthor":false,"prefix":"","firstName":"Volodin","middleName":"","lastName":"Andrei","suffix":""},{"id":625072422,"identity":"4998d893-51e4-4ed4-b6e4-37e7cdcb741b","order_by":2,"name":"Xuejun Wang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAu0lEQVRIiWNgGAWjYHCCBGYGNgY5NvbmA6RpMebjOZZAvDUgLYnzJHIUiFNucCPh4eeCssPpbQw5DAw/KrYRoeXMgWTpGefSctsYzh5g7Dlzm7AWs+MNCdK8bTa5bYx9CcyMbcRoOcyQ/Ju3TSKdjZnHgEgtxxvSQLYksLERq8X+zIE0a55zaYZtPGwJB4nyi+SMnOTbPGWH5eXnPz744EcFEVoYGHgS4MwDxKgHAnZiFY6CUTAKRsGIBQCp5DmB5dXHFgAAAABJRU5ErkJggg==","orcid":"","institution":"Anhui University","correspondingAuthor":true,"prefix":"","firstName":"Xuejun","middleName":"","lastName":"Wang","suffix":""}],"badges":[],"createdAt":"2026-04-14 10:11:20","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9414003/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9414003/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107869180,"identity":"1d4346aa-768e-48ec-8627-ecb8b9ca2cab","added_by":"auto","created_at":"2026-04-27 07:36:20","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":296764,"visible":true,"origin":"","legend":"","description":"","filename":"sourcefiles.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9414003/v1_covered_cf41893d-a74f-4fea-aa7a-58a178cc8840.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eComplete \u003cem\u003ef\u003c/em\u003e-moment convergence for arrays of rowwise \u003cem\u003em\u003c/em\u003e\u003csub\u003e\u003cem\u003en\u003c/em\u003e\u003c/sub\u003e-extended negatively dependent random variables and its application\u003c/p\u003e","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":"methodology-and-computing-in-applied-probability","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"mcap","sideBox":"Learn more about [Methodology and Computing in Applied Probability](http://link.springer.com/journal/11009)","snPcode":"11009","submissionUrl":"https://submission.nature.com/new-submission/11009/3","title":"Methodology and Computing in Applied Probability","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"rowwise mn-extended negatively dependent random variables, complete fmoment convergence, maximal weighted sums, nonparametric regression models, complete consistency","lastPublishedDoi":"10.21203/rs.3.rs-9414003/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9414003/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAs a key branch of probability theory and mathematical statistics, probability limit theory focuses on analyzing the convergence properties of random variable sequences and their associated distribution functions. 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