A Modified Likelihood Ratio Test for Homogeneity in the Finite Mixture Models

Abstract

The problem of testing the homogeneity in the context of finite mixture models has been discussed by many authors recently. There has been great advances in deriving the limiting distributions of the likelihood ratio test statistics for various finite mixture models. While these results contribute greatly to our understanding of the nature of the problem, the limiting distributions are often too complex to have significant applicational values. In this paper, we propose a modified likelihood ratio test for homogeneity in the finity mixture models of a general parametric distribution family. We show that the modified statistics have simple limiting distributions. At local alternative models, the new procedure and the well known C(α) method are equivalent. However, the modified likelihood ratio test is more powerful for general alternatives. Our simulation reveals that the limiting distributions offer satisfactory approximations to the quantiles of the modified likelihood ratio test statistic at moderate sample size. We further illustrate that the modified likelihood ratio test is far more powerful than the C(α) test for some finite mixture models. This talk is based on a joint work with Hanfeng Chen and John, D. Kalbfleisch.