CONSTRAINED MAXIMUM-LIKELIHOOD ESTIMATION FOR A MIXTURE OF M UNIVARIATE NORMAL DISTRIBUTIONS
HATHAWAY, RICHARD JOSEPH
Doctor of Philosophy
A straightforward application of the method of maximum likelihood to a mixture of normal distributions leads to an ill-posed optimization problem. In the univariate case, adding simple constraints on the component standard deviations of the form (sigma)(,i) (GREATERTHEQ) c (sigma)(,i+1) transforms the ill-posed problems into one that is both optimizationally and statistically well posed; a global maximizer of the likelihood function exists and is strongly consistent. Combining the above constraints with the EM algorithm leads to an algorithm that requires little additional work per iteration and offers superior convergence properties. The results of numerical tests indicate that the constrained EM algorithm produces reasonable estimates more often than other algorithms.