“Maximum likelihood estimation for linear Gaussian covariance models” to appear in Journal of Royal Statistical Society – Series B
In a new paper Piotr Zwiernik, Caroline Uhler, and Donald Richards study the Gaussian models with linear structure of the covariance matrix. 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, they provide sufficient conditions for any hill-climbing method to converge to the global maximum. An important consequence of this analysis is that for sample sizes n≃14p, maximum likelihood estimation for linear Gaussian covariance models behaves as if it were a convex optimization problem. The paper is going to appear in Journal of Royal Statistical Society – Series B; the arXiv version is available here.