{"paper_id":"1c1f2bcd-4487-4d0f-a445-b4001bea8273","body_text":"Extension of ratio-type estimators for sensitive variables under measurement error and non-response via median ranked-set sampling | 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 Extension of ratio-type estimators for sensitive variables under measurement error and non-response via median ranked-set sampling Mohammad Hossein Zarinkolah, Hadi Jabbari, Mohammad Mehdi Saber This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7836836/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 Estimating the mean of sensitive variables—such as Drug use—is often challenged by non-response and measurement error. To address these issues, we propose a novel two-phase hybrid estimation framework that integrates median ranked-set sampling (MRSS) and simple random sampling without replacement (SRSWOR), leveraging one or two auxiliary variables to improve the estimation accuracy. The key innovation lies in the strategic combination of MRSS and SRSWOR, tailored to the response dynamics of each phase. Under standard regularity conditions, we derive approximate expressions for bias and mean squared error (MSE) using Taylor expansion. The proposed estimators are validated through simulation studies and applied to estimate the average number of cigarettes smoked daily among university students, using time spent with friends as an auxiliary variable. Our analysis reveals that MRSS offers superior performance in the initial sampling phase, particularly when response rates are low, while SRSWOR is advantageous in the second phase if subsampling proportional to the response rate λ is feasible. In scenarios where full response in the second phase is unattainable, MRSS consistently yields lower MSE. Limitations of the proposed approach include reliance on accurate auxiliary information, the assumption of independence between sampling phases, and the requirement of population symmetry for theoretical derivations involving MRSS. The results underscore the practical utility and robustness of the proposed approach in handling sensitive survey data. Subject Classification: 62D05, 62D99 Median ranked-set sampling sensitive variable ratio estimation measurement error non-response sampling surveys Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Reviews received at journal 30 Oct, 2025 Reviewers agreed at journal 24 Oct, 2025 Reviewers agreed at journal 23 Oct, 2025 Reviewers invited by journal 23 Oct, 2025 Editor assigned by journal 14 Oct, 2025 Submission checks completed at journal 14 Oct, 2025 First submitted to journal 11 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. 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-7836836\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":false,\"archivedVersions\":[],\"articleType\":\"Research Article\",\"associatedPublications\":[],\"authors\":[{\"id\":538749284,\"identity\":\"52e88cb1-9faf-4b0d-a846-d2287bb2db9d\",\"order_by\":0,\"name\":\"Mohammad Hossein Zarinkolah\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Ferdowsi University of Mashhad\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Mohammad\",\"middleName\":\"Hossein\",\"lastName\":\"Zarinkolah\",\"suffix\":\"\"},{\"id\":538749285,\"identity\":\"67a1d1d9-c5b0-4e5e-9ea0-1cf92d522623\",\"order_by\":1,\"name\":\"Hadi 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To address these issues, we propose a novel two-phase hybrid estimation framework that integrates median ranked-set sampling (MRSS) and simple random sampling without replacement (SRSWOR), leveraging one or two auxiliary variables to improve the estimation accuracy. The key innovation lies in the strategic combination of MRSS and SRSWOR, tailored to the response dynamics of each phase. Under standard regularity conditions, we derive approximate expressions for bias and mean squared error (MSE) using Taylor expansion. The proposed estimators are validated through simulation studies and applied to estimate the average number of cigarettes smoked daily among university students, using time spent with friends as an auxiliary variable. Our analysis reveals that MRSS offers superior performance in the initial sampling phase, particularly when response rates are low, while SRSWOR is advantageous in the second phase if subsampling proportional to the response rate λ is feasible. 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