Quandt and Ramsey have suggested an estimator for normal mixtures and switching regressions, which minimizes a sum of squared differences between empirical and theoretical values of the moment generating function. This paper demonstrates how their estimator can be improved by minimizing a generalized sum of squares rather than an ordinary sum of squares. When this is done, more points of evaluation (moments) are unambiguously better than less. Most of the results presented are also applicable to method of moments estimators in general.

Michael Thomson, Peter Schmidt, A Note on the Comparison of the Mean Square Error of Inequality Constrained Least Squares and Other Related Estimators, The Review of Economics and Statistics, Vol. 64, No. 1 (Feb., 1982), pp. 174-176