Minimum Distance Estimation of Mixture Model Parameters - Asymptotic Results and Simulation Comparisons with Maximum Likelihood.

Abstract : The estimation of mixing proportions in the mixture model is discussed with emphasis on the mixture of two normal components with all five parameters unknown. Simulations are presented which compare minimum distance (MD) and maximum likelihood (ML) estimation of the parameters of this mixture-of-normals model. Some practical issues of implementation of these results are also discussed. Simulation results indicate that ML techniques are superior to MD when component distributions actually are normal, while MD techniques provide better estimates than ML under symmetric departures from component normality. Results are presented which establish strong consistency and asymptotic normality of the MD estimator under conditions which include the mixture-of-normals model. Asymptotic variances and relative efficiencies are obtained for further comparison of the MDE and MLE. (Author)