Details:
Title  Counting and locating the solutions of polynomial systems of maximum likelihood equations, I  Author(s)  MaxLouis G. Buot, Donald St.  Type  Article in Journal  Abstract  In statistical inference, mixture models consisting of several component subpopulations are used widely to model data drawn from heterogeneous sources. In this paper, we consider maximum likelihood estimation for mixture models in which the only unknown parameters are the component proportions. By applying the theory of multivariable polynomial equations, we derive bounds for the number of isolated roots of the corresponding system of likelihood equations. If the component densities belong to certain familiar continuous exponential families, including the multivariate normal or gamma distributions, then our upper bound is, almost surely, the exact number of solutions.  Keywords  Bernstein’s theorem, Carrier sets, EM algorithm, Facial resultant, Finite mixture model, Genetic algorithms, Homotopy continuation methods, Maximum likelihood estimation, Mixed volume, Numerical continuation algorithms  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717105001197 
Language  English  Journal  Journal of Symbolic Computation  Volume  41  Number  2  Pages  234  244  Year  2006  Note  Computational Algebraic Statistics Computational Algebraic Statistics  Edition  0  Translation 
No  Refereed 
No 
