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• W2008330147 abstract "We consider regularized covariance estimation in scaled Gaussian settings, e.g., elliptical distributions, compound-Gaussian processes and spherically invariant random vectors. Asymptotically in the number of samples, the classical maximum likelihood (ML) estimate is optimal under different criteria and can be efficiently computed even though the optimization is nonconvex. We propose a unified framework for regularizing this estimate in order to improve its finite sample performance. Our approach is based on the discovery of hidden convexity within the ML objective. We begin by restricting the attention to diagonal covariance matrices. Using a simple change of variables, we transform the problem into a convex optimization that can be efficiently solved. We then extend this idea to nondiagonal matrices using convexity on the manifold of positive definite matrices. We regularize the problem using appropriately convex penalties. These allow for shrinkage towards the identity matrix, shrinkage towards a diagonal matrix, shrinkage towards a given positive definite matrix, and regularization of the condition number. We demonstrate the advantages of these estimators using numerical simulations." @default.
• W2008330147 created "2016-06-24" @default.
• W2008330147 creator A5091732723 @default.
• W2008330147 date "2012-01-01" @default.
• W2008330147 modified "2023-09-26" @default.
• W2008330147 title "Unified Framework to Regularized Covariance Estimation in Scaled Gaussian Models" @default.
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• W2008330147 doi "https://doi.org/10.1109/tsp.2011.2170685" @default.
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