A Group Sequential Sampling Approach for the Behrens-Fisher Problem with Suspected Outliers in Data

A Group Sequential Sampling Approach for the Behrens-Fisher Problem with Suspected Outliers in 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 A Group Sequential Sampling Approach for the Behrens-Fisher Problem with Suspected Outliers in Data Ashwani Rajput, Neeraj Joshi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8504949/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 take another look at the Behrens-Fisher Problem, which is a widely recognized problem in statistical literature. In fact, we work on a variant of the classical Behrens-Fisher problem setup, where we test whether the difference of two normal means equals a specified threshold value under the assumption of unknown and unequal variances. Under the proposed hypothesis testing framework, our aim is to control type I and type II error probabilities by imposing upper bounds on them. We establish that the resulting optimal fixed sample size depends on the unknown standard deviations, making the desired testing accuracies impossible to achieve. Therefore, we take a sequential hypothesis testing route and implement a group sequential sampling strategy to tackle the proposed testing problem. The associated termination rule (a random sample size used to estimate the optimal fixed sample size) is defined by using the improved classes of unbiased estimators for the population standard deviations instead of the customary sample standard deviations. This makes our sequential rule more robust under possible outlying observations in the data. We study several interesting properties of the proposed estimators and the subsequent sequential termination rule. Our group sequential sampling strategy proves to be first-order efficient and consistent. The extensive simulations and a real data illustration regarding diabetes patients further support our theoretical findings and highlight the practical relevance of the proposed methodology. Mathematics Subject Classifications: 62L12, 62F03, 62F05 Behrens-Fisher Problem Gini’s Mean Difference Group Sequential Sampling Hypothesis Testing Mean Absolute Deviation Outliers 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. 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