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Maximum likelihood estimation for this class of models leads to a non-convex optimization problem which typically has many local maxima. Using recent results on the asymptotic distribution of extreme eigenvalues of the Wishart distribution, we provide sufficient conditions for any hill climbing method to converge to the global maximum. Although we are primarily interested in the case in which n \u226b p, the proofs of our results utilize large sample asymptotic theory under the scheme n\/p \u2192 \u03b3 &amp;gt; 1. Remarkably, our numerical simulations indicate that our results remain valid for p as small as 2. An important consequence of this analysis is that, for sample sizes n\u224314p, maximum likelihood estimation for linear Gaussian covariance models behaves as if it were a convex optimization problem.<\/jats:p>","DOI":"10.1111\/rssb.12217","type":"journal-article","created":{"date-parts":[[2016,11,3]],"date-time":"2016-11-03T10:16:48Z","timestamp":1478168208000},"page":"1269-1292","source":"Crossref","is-referenced-by-count":36,"title":["Maximum Likelihood Estimation for Linear Gaussian Covariance Models"],"prefix":"10.1093","volume":"79","author":[{"given":"Piotr","family":"Zwiernik","sequence":"first","affiliation":[{"name":"Universitat Pompeu Fabra , Barcelona , Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Caroline","family":"Uhler","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology , Cambridge , USA"},{"name":"Institute of Science and Technology Austria , Klosterneuburg , Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Donald","family":"Richards","sequence":"additional","affiliation":[{"name":"Penn State University , University Park , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2016,11,3]]},"reference":[{"key":"2023021801093682000_rssb12217-cit-0001","first-page":"1","volume-title":"Essays in Probability and Statistics","author":"Anderson","year":"1970"},{"key":"2023021801093682000_rssb12217-cit-0002","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1214\/aos\/1193342389","article-title":"Asymptotically efficient estimation of covariance matrices with linear structure","volume":"1","author":"Anderson","year":"1973","journal-title":"Ann. 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