Likelihood-Based Inference with Separable Correlation Matrices

[1805.00318] Likelihood-Based Inference with Separable Correlation Matrices Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Statistics > Computation arXiv:1805.00318 (stat) [Submitted on 1 May 2018 ( v1 ), last revised 14 Apr 2026 (this version, v3)] Title: Likelihood-Based Inference with Separable Correlation Matrices Authors: Karl Oskar Ekvall View a PDF of the paper titled Likelihood-Based Inference with Separable Correlation Matrices, by Karl Oskar Ekvall View PDF HTML (experimental) Abstract: This paper proposes methods for likelihood-based inference in multivariate linear regressions when the correlation matrix of the responses is separable; that is, it has a Kronecker product structure, but the variances are unrestricted. The methods are enabled by a block-coordinate ascent-like algorithm with closed-form updates that strictly increases the likelihood at every iteration until convergence. In the numerical experiments, the proposed algorithm is 300--2500 times faster than a general-purpose solver, making parametric bootstrap tests of correlation and covariance separability practical. Parameters are identifiable, and standard errors can therefore be obtained from the expected Fisher information, which can be computed efficiently using the Kronecker product structure. Simulations show that the proposed estimator has lower error than both separable covariance and unrestricted estimators when the model holds, and that bootstrap tests maintain nominal size where asymptotic tests fail. An application to dissolved oxygen data from the Mississippi River demonstrates that separable correlation captures location-specific variance patterns that separable covariance cannot. Subjects: Computation (stat.CO) Cite as: arXiv:1805.00318 [stat.CO] (or arXiv:1805.00318v3 [stat.CO] for this version) https://doi.org/10.48550/arXiv.1805.00318 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Karl Oskar Ekvall [ view email ] [v1] Tue, 1 May 2018 13:20:14 UTC (234 KB) [v2] Mon, 7 May 2018 15:10:18 UTC (231 KB) [v3] Tue, 14 Apr 2026 18:44:17 UTC (53 KB) Full-text links: Access Paper: View a PDF of the paper titled Likelihood-Based Inference with Separable Correlation Matrices, by Karl Oskar Ekvall View PDF HTML (experimental) TeX Source view license Current browse context: stat.CO < prev | next > new | recent | 2018-05 Change to browse by: stat References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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