Mean and Sparse Covariance Monitoring via Maximum Likelihood Estimation with Positive-Definite Thresholding

Mean and Sparse Covariance Monitoring via Maximum Likelihood Estimation with Positive-Definite Thresholding | 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 Method Article Mean and Sparse Covariance Monitoring via Maximum Likelihood Estimation with Positive-Definite Thresholding Derek Weix, Nicholas C. Taylor, Rakheon Kim, Tzahi Y. Cath, Amanda S. Hering This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9247228/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 Multivariate statistical process monitoring is used to detect changes in the distribution of a multivariate process in real time. With modern systems, the number of variables being recorded and the complexity of their interactions are increasing. As the dimension of a process increases, the number of parameters required to estimate the covariance matrix increases quadratically; however, not every pair of monitored variables are related. In such cases, there is no need to estimate their covariance. We propose two new control charts that monitor shifts in the covariance and/or the mean and covariance of a multivariate process and that employ a sparse covariance estimation technique to reduce the number of parameters that must be estimated. This estimator is asymptotically efficient, consistent, and guaranteed positive-definite. When compared with competitors in a simulation study, methods based on this estimator produce a similar detection rate for shifts in the mean and/or variance and a superior detection rate for shifts in the covariance. Furthermore, this estimator has a substantially faster execution time, which is advantageous when deployed in real time. These methods are demonstrated on a case study of a fault that was deliberately introduced into a direct potable reuse water treatment system. Covariance Monitoring Maximum Likelihood Estimation Multivariate Process Water Treatment Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 06 May, 2026 Reviewers agreed at journal 01 May, 2026 Reviewers invited by journal 22 Apr, 2026 Editor assigned by journal 22 Apr, 2026 Editor invited by journal 13 Apr, 2026 Submission checks completed at journal 12 Apr, 2026 First submitted to journal 12 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-9247228","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Method Article","associatedPublications":[],"authors":[{"id":630207691,"identity":"e083ee55-43b8-4bde-aefa-57cc48142565","order_by":0,"name":"Derek Weix","email":"","orcid":"","institution":"Baylor University","correspondingAuthor":false,"prefix":"","firstName":"Derek","middleName":"","lastName":"Weix","suffix":""},{"id":630207700,"identity":"93ee7c32-8701-4cea-b3df-93637a6fad14","order_by":1,"name":"Nicholas C. 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