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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
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717105001136
LanguageEnglish
JournalJournal of Symbolic Computation
Volume41
Number2
Pages245 - 254
Year2006
NoteComputational Algebraic Statistics Computational Algebraic Statistics
Edition0
Translation No
Refereed No
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