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TitleComputing all roots of the likelihood equations of seemingly unrelated regressions
Author(s) Mathias Drton
TypeArticle in Journal
AbstractSeemingly 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.
KeywordsAlgebraic statistics, Gröbner basis, Maximum likelihood estimation, Multivariate statistics, Seemingly unrelated regressions
URL http://www.sciencedirect.com/science/article/pii/S0747717105001136
JournalJournal of Symbolic Computation
Pages245 - 254
NoteComputational Algebraic Statistics Computational Algebraic Statistics
Translation No
Refereed No