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Estimating linear
covariance models with numerical nonlinear algebra
Bernd Sturmfels, Sascha Timme and Piotr Zwiernik |
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Vol. 11 (2020), No. 1, 31–52
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Abstract |
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Numerical nonlinear algebra is applied to maximum likelihood estimation for Gaussian models defined by linear constraints on the covariance matrix. We examine the generic case as well as special models (e.g., Toeplitz, sparse, trees) that are of interest in statistics. We study the maximum likelihood degree and its dual analogue, and we introduce a new software package LinearCovarianceModels.jl for solving the score equations. All local maxima can thus be computed reliably. In addition we identify several scenarios for which the estimator is a rational function. |
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Keywords
linear covariance model, maximum likelihood, dual maximum
likelihood, numerical nonlinear algebra
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Mathematical Subject Classification 2010
Primary: 14Q99, 62F10
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Milestones
Received: 4 September 2019
Revised: 23 January 2020
Accepted: 30 April 2020
Published: 1 October 2020
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Authors |
| Bernd Sturmfels | |
| Max Planck-Institute for Mathematics
in the Sciences Leipzig Germany |
Department of Mathematics University of California, Berkeley Berkeley, CA United States |
| Sascha Timme | |
| Institut für Mathematik Technische Universität Berlin Berlin Germany |
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| Piotr Zwiernik | |
| Department of Economics and
Business Universitat Pompeu Fabra Barcelona Spain |
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