TESTING FOR THE NUMBER OF COMPONENTS IN A MIXTURE OF NORMAL-DISTRIBUTIONS USING MOMENT ESTIMATORS

We develop two procedures based on the moment estimators that can be used to test for the number of component distributions in a mixture of normal distributions with equal variances. One is a computationally fast moment version of the likelihood ratio procedure. We apply these procedures to the classic problem of testing for the presence of two normal components versus a null hypothesis of normality. Our simulations show that these test procedures arc quite powerful for many mixture alternatives, and, most importantly, that the moment version of the likelihood procedure is almost as powerful as the likelihood ratio test.