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Our proposed estimation method solves a convex problem and yields an M-estimator, allowing for relatively straightforward asymptotic (in general) and finite sample analysis (in the Gaussian case). In particular, we recover standard n\/d rates, where d is the dimension of the underlying model. Our geometric insights allow to extend various recent results in covariance matrix modelling. This includes providing unrestricted parametrizations of the space of correlation matrices, which is alternative to a recent result utilizing the matrix logarithm.<\/jats:p>","DOI":"10.1214\/24-aos2474","type":"journal-article","created":{"date-parts":[[2025,9,12]],"date-time":"2025-09-12T05:22:31Z","timestamp":1757654551000},"page":"1371-1405","source":"Crossref","is-referenced-by-count":1,"title":["Entropic covariance models"],"prefix":"10.1214","volume":"53","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3431-131X","authenticated-orcid":false,"given":"Piotr","family":"Zwiernik","sequence":"first","affiliation":[{"name":"Department of Statistical Sciences, University of Toronto"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"108","reference":[{"key":"20","doi-asserted-by":"crossref","unstructured":"Boik, R. J.<\/small> (2002). Spectral models for covariance matrices. 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