em-Test for Homogeneity

Abstract

The modified likelihood ratio test represents a significant advancement over the limitations of conventional likelihood ratio tests. It is applicable to a specific class of finite mixture models, although its success remains somewhat constrained. An interesting variation of this test is the EM-test, which may be seen as a derivative of the modified likelihood ratio test. In contrast to comparing the maximum possible modified likelihood values under null and alternative hypotheses concerning the order of the finite mixture model, the EM-test focuses on how quickly the likelihood increases when using EM-iterations from the best-fitted null model in a specific manner. This chapter introduces the concept and the conclusions related to the simple homogeneity case, with the more complex scenarios addressed in the subsequent chapter. It unveils the somewhat more intricate technical advantages of this approach.