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However, if the assumption of separability is not met, data analysis with a separable model may misrepresent important dependence patterns in the data. As a compromise between separable and unstructured covariance estimation, we decompose a covariance matrix into a separable component and a complementary \u2018core\u2019 covariance matrix. This decomposition defines a new covariance matrix decomposition that makes use of the parsimony and interpretability of a separable covariance model, yet fully describes covariance matrices that are non-separable. This decomposition motivates a new type of shrinkage estimator, obtained by appropriately shrinking the core of the sample covariance matrix, that adapts to the degree of separability of the population covariance matrix.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkad070","type":"journal-article","created":{"date-parts":[[2023,6,29]],"date-time":"2023-06-29T11:52:02Z","timestamp":1688039522000},"page":"1659-1679","source":"Crossref","is-referenced-by-count":9,"title":["Core shrinkage covariance estimation for matrix-variate data"],"prefix":"10.1093","volume":"85","author":[{"given":"Peter","family":"Hoff","sequence":"first","affiliation":[{"name":"Department of Statistical Science, Duke University , Durham , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4938-1812","authenticated-orcid":false,"given":"Andrew","family":"McCormack","sequence":"additional","affiliation":[{"name":"Department of Statistical Science, Duke University , Durham , 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