On semiparametric generalized linear models with nonparametric canonical link

On semiparametric generalized linear models with nonparametric canonical link | 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 On semiparametric generalized linear models with nonparametric canonical link Busayasachee Puang-Ngern, Wandee Wanishsakpong, Jun Ma This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8962870/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 6 You are reading this latest preprint version Abstract Since the seminal paper by Nelder and Wedderburn (1972), generalized linear models (GLMs) have become a popular option for building regression models. Although GLMs offer a rich family of distributions and link functions, modellers often encounter the perplexing challenge of finding a suitable combination of response distribution and link function that yields a satisfactory fit to the data. The semiparametric GLM is a useful and powerful alternative as it offers flexibility in the response distribution , but it still requires specifications of a link function and its maximum likelihood computation is difficult. In this paper, we propose a novel extension of the semiparametric GLM in which the link function is required to be canonical, but its functional form is left unspecified. That is, the link function is unknown (apart from the canonical requirement) and is determined nonparametrically from the data. Semiparametric generalized linear models canonical link maximum likelihood estimation constrained optimisation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 04 Mar, 2026 Reviewers agreed at journal 04 Mar, 2026 Reviewers invited by journal 04 Mar, 2026 Editor assigned by journal 26 Feb, 2026 Submission checks completed at journal 26 Feb, 2026 First submitted to journal 24 Feb, 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-8962870","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":600904406,"identity":"77ef3129-af26-4b1f-a2e0-456d4fee789e","order_by":0,"name":"Busayasachee Puang-Ngern","email":"","orcid":"","institution":"Chulalongkorn University","correspondingAuthor":false,"prefix":"","firstName":"Busayasachee","middleName":"","lastName":"Puang-Ngern","suffix":""},{"id":600904407,"identity":"fdcc2222-67f0-4cc6-a6f8-364fe9da219b","order_by":1,"name":"Wandee Wanishsakpong","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAArUlEQVRIiWNgGAWjYJACCRDBzwMkGBtI0SLZAyQOkqTF4AyxWgyOnz1440MFQ+LmM2cMmD/uIEbLmbxkyxlnGBK3ne0xYDh4hggtZgdyzKR52xhyt53nAWppI0bL+Tdm0n//MeRu7idayw2gLcCwzd3A20OkFvsbb4wte45J1M84c6zgwFlitEj25xje+FFjY8zfk7zxQSUxWqAAHDUMB4jXMApGwSgYBaMALwAAY9c5+pLKiiAAAAAASUVORK5CYII=","orcid":"","institution":"Kasetsart University","correspondingAuthor":true,"prefix":"","firstName":"Wandee","middleName":"","lastName":"Wanishsakpong","suffix":""},{"id":600904408,"identity":"a7ed9803-73ee-4b3e-9471-08fe622cfa15","order_by":2,"name":"Jun Ma","email":"","orcid":"","institution":"Macquarie University","correspondingAuthor":false,"prefix":"","firstName":"Jun","middleName":"","lastName":"Ma","suffix":""}],"badges":[],"createdAt":"2026-02-25 04:08:27","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8962870/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8962870/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104403860,"identity":"647178a4-9713-4e76-bfa7-942be949cebf","added_by":"auto","created_at":"2026-03-11 12:19:14","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":397210,"visible":true,"origin":"","legend":"","description":"","filename":"Onsemiparametricgeneralizedlinearmodelswithnonparametriccanonicallink.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8962870/v1_covered_3ca71d66-39ff-4f6f-8a3f-6eb7ff4aacfc.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"On semiparametric generalized linear models with nonparametric canonical link","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":"Semiparametric generalized linear models, canonical link, maximum likelihood estimation, constrained optimisation","lastPublishedDoi":"10.21203/rs.3.rs-8962870/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8962870/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Since the seminal paper by Nelder and Wedderburn (1972), generalized linear models (GLMs) have become a popular option for building regression models. 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