A comparison of minimum distance and maximum likelihood estimation of a mixture proportion. (English) Zbl 0547.62017

Woodward, Wayne A.; Parr, William C.; Schucany, William R.; Lindsey, Hildegard

J. Am. Stat. Assoc. 79, 590-598 (1984).

Summary: 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 that 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, but MD techniques provide better estimates than ML under symmetric departures from component normality.
Interestingly, an ad hoc starting value for the iterative procedures occasionally outperformed both the ML and MD techniques. Results are presented that establish strong consistency and asymptotic normality of the MD estimator under conditions that include the mixture-of-normals model. Asymptotic variances and relative efficiencies are obtained for further comparison of the MD and ML estimators.

MSC:

62F10	Point estimation
62F12	Asymptotic properties of parametric estimators
65C05	Monte Carlo methods

Keywords:

robustness; EM algorithm; estimation of mixing proportions; mixture model; normal components; minimum distance; maximum likelihood; iterative procedures; strong consistency; asymptotic normality; Asymptotic variances; relative efficiencies