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Estimating linear covariance models with numerical nonlinear algebra

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arxiv 1909.00566 v1 pith:34A6VHPV submitted 2019-09-02 stat.CO math.AG

Bernd Sturmfels , Sascha Timme , Piotr Zwiernik This is my paper
classification stat.COmath.AG
keywords modelsalgebracovariancelikelihoodlinearmaximumnonlinearnumerical
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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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Cited by 1 Pith paper

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  1. Likelihood Geometry of Moving Average and Autoregressive Processes

    math.ST 2026-07 accept novelty 6.0 of 10

    The parametric ML degree of MA(1) is 8(n−1); non-invertible critical points for MA(1)/MA(2) are classified with closed forms, and analogous algebraic degrees are computed for composite likelihood and AR models.

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