MEASURING THE RELATIVE EFFECTIVENESS OF MOMENT ESTIMATORS AS STARTING VALUES IN MAXIMIZING LIKELIHOODS

We consider the vexing computational problem of estimating the parameters of a mixture of two normal distributions with equal variances using maximum likelihood estimation- As a partial solution we reconsider the strongly consistent moment estimators as starting values for the likelihood maximization algorithms. Using a technique based on the determinantal properties of certain matrices of moments one can solve the moment equations in a surprisingly straightforward manner. Finally, our simulation results indicate that the moment estimators compare favorably to the actual values of the parameters in terms of their effectiveness as starting values in maximizing mixture likelihoods.