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Maximum likelihood
degree of the two-dimensional linear Gaussian covariance
model
Jane Ivy Coons, Orlando Marigliano and Michael Ruddy |
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Vol. 11 (2020), No. 2, 107–123
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Abstract |
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In algebraic statistics, the maximum likelihood degree of a statistical model is the number of complex critical points of its log-likelihood function. A priori knowledge of this number is useful for applying techniques of numerical algebraic geometry to the maximum likelihood estimation problem. We compute the maximum likelihood degree of a generic two-dimensional subspace of the space of Gaussian covariance matrices. We use the intersection theory of plane curves to show that this number is . |
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Keywords
algebraic geometry, algebraic statistics, linear Gaussian
covariance models, intersection theory, plane curves,
maximum likelihood estimation, maximum likelihood degree
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Mathematical Subject Classification 2010
Primary: 13P25, 14C17, 14H50, 62H12
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Milestones
Received: 10 September 2019
Revised: 20 May 2020
Accepted: 8 June 2020
Published: 28 December 2020
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Authors |
| Jane Ivy Coons | |
| Department of Mathematics North Carolina State University Raleigh, NC United States |
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| Orlando Marigliano | |
| Max-Planck-Institute for Mathematics
in the Sciences Leipzig Germany |
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| Michael Ruddy | |
| Max-Planck-Institute for Mathematics
in the Sciences Leipzig Germany |
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