Testing the Order of a Finite Mixture
Pengfei Li, Jiahua Chen · Journal of the American Statistical Association · 2010
The order is an important parameter in applications of finite mixture models. Yet designing a valid and easy-to-use statistical test for the order is challenging. To date, most results on hypothesis tests have focused on homogeneity, a special case where the null model has order 1. In this work, we designed an EM test for the general problem of testing the null hypothesis of order m0 versus an alternative hypothesis of order larger than m0. For any positive integer m0, the null limiting distribution of the EM test is a mixture of χ2 distributions. The weights in this mixture-limiting distribution can be conveniently computed. Compared with related results, the new result is obtained under much less strict requirements on the component distribution and the parameter space. Extensive simulation studies show that the limiting distributions closely match the finite sample distributions of the EM test. When m0 = 2, the new EM test has more accurate type I errors and matches the power of the modified likelihood ratio test. When m0 = 3, there is a clear indication that the test has good power properties. Supplementary materials for this article are available online.