Details:
Title  Computing all roots of the likelihood equations of seemingly unrelated regressions  Author(s)  Mathias Drton  Type  Article in Journal  Abstract  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.  Keywords  Algebraic statistics, Gröbner basis, Maximum likelihood estimation, Multivariate statistics, Seemingly unrelated regressions  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717105001136 
Language  English  Journal  Journal of Symbolic Computation  Volume  41  Number  2  Pages  245  254  Year  2006  Note  Computational Algebraic Statistics Computational Algebraic Statistics  Edition  0  Translation 
No  Refereed 
No 
