On the Power of Different Versions of the Likelihood Ratio Test for Homogeneity in an Exponential Mixture Model

In a model of mixtures of exponentials, we consider the likelihood ration test for homogeneity against the alternative that there are two mixture components. As the likelihood function under the alternative is not unimodal, different choices of starting values for likelihood maximization yield different tests. We simulate the power of several versions of these tests for a variety of alternatives and sample sizes. The ranking of the tests is the same in all instances; in particular, a multistart version that comes near to global maximization never yields the the largest power. The largest power is always achieved by two simple strategies each of which starts from one single initial value.