2005/08/23 by Mathias Drton, Drton, Mathias
Computer Science · Engineering · Mathematics · #62H12 #62J05 #Bayesian Modeling and Causal Inference #Control Systems and Identification #FOS: Mathematics #Polynomial and algebraic computation #Statistics Theory (math.ST) #math.ST #msc:62H12 #msc:62J05 #stat.TH
paper · pdf · doi:10.48550/arxiv.math/0508437
To appear in the Journal of Symbolic Computation, special issue on Computational Algebraic Statistics. 11 pages
arxiv created 2005/08/23 · openalex publication_date 2005/08/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Seemingly unrelated regressions are statistical regression models based on the Gaussian distribution. They are popular in econometrics but also arise in graphical modeling of multivariate dependencies. In maximum likelihood estimation, the parameters of the model are estimated by maximizing the likelihood function, which maps the parameters to the likelihood of observing the given data. By transforming this optimization problem into a polynomial optimization problem, it was recently shown that the likelihood function of a simple bivariate seemingly unrelated regressions model may have several stationary points. Thus local maxima may complicate maximum likelihood estimation. In this paper, we study several more complicated seemingly unrelated regression models, and show how all stationary points of the likelihood function can be computed using algebraic geometry.