Stochastic approximation method for kernel sliced average variance estimation

Stochastic approximation method for kernel sliced average variance 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 Stochastic approximation method for kernel sliced average variance estimation Emmanuel De Dieu Nkou This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8463599/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 In this paper, we use the stochastic approximation method to estimate Sliced Average Variance Estimation (SAVE). This method is known for its efficiency in recursive estimation. Stochastic approximation is particularly effective for constructing recursive estimators and has been widely used in density estimation, regression, and semi-parametric models. We prove that the resulting estimator is asymptotically normal and root $n$ consistent. Through simulations conducted in the laboratory and applied to real data, we show that it is faster than the kernel method previously proposed. Mathematics subject classification 2020: 62H12; 62J02; 62E20; 62G05. stochastic approximation algorithm dimension reduction asymptotic normality semiparametric regression 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-8463599","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":584608350,"identity":"6dfbf865-f742-45b5-96d3-476b5bb6c7cf","order_by":0,"name":"Emmanuel De Dieu Nkou","email":"data:image/png;base64,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","orcid":"","institution":"Université des Sciences et Techniques de Masuku","correspondingAuthor":true,"prefix":"","firstName":"Emmanuel","middleName":"De Dieu","lastName":"Nkou","suffix":""}],"badges":[],"createdAt":"2025-12-28 02:38:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8463599/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8463599/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105070085,"identity":"59f01ff0-2de6-4d10-bcfe-324e2a32d123","added_by":"auto","created_at":"2026-03-20 14:55:36","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":370480,"visible":true,"origin":"","legend":"","description":"","filename":"SaveRecursive.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8463599/v1_covered_0177d39a-2aae-4736-88d6-4b1a0b32e512.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eStochastic approximation method for kernel sliced average variance estimation\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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":"stochastic approximation algorithm, dimension reduction, asymptotic normality, semiparametric regression","lastPublishedDoi":"10.21203/rs.3.rs-8463599/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8463599/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this paper, we use the stochastic approximation method to estimate Sliced Average Variance Estimation (SAVE). This method is known for its efficiency in recursive estimation. Stochastic approximation is particularly effective for constructing recursive estimators and has been widely used in density estimation, regression, and semi-parametric models. We prove that the resulting estimator is asymptotically normal and root $n$ consistent. Through simulations conducted in the laboratory and applied to real data, we show that it is faster than the kernel method previously proposed.\u003c/p\u003e\n\u003cp\u003eMathematics subject classification 2020: 62H12; 62J02; 62E20; 62G05.\u003c/p\u003e","manuscriptTitle":"Stochastic approximation method for kernel sliced average variance estimation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-04 22:21:23","doi":"10.21203/rs.3.rs-8463599/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":"0a1b6bbd-d0ee-4913-991e-bef7e93e1a40","owner":[],"postedDate":"February 4th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-03-20T14:53:14+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-04 22:21:23","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8463599","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8463599","identity":"rs-8463599","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}