A Modified Likelihood Ratio Test For Homogeneity in Finite Mixture Models

Testing for homogeneity in finite mixture models has been investigated recently by many authors. It has been recognized that the asymptotic null distribution of the likelihood ratio test (LRT) is very complex and difficult to implement. In this paper, we propose a modified LRT for homogeneity in the finite mixture models with a general parametric kernel distribution family. The modified LRT enjoys the simple X2- type null limiting distribution and is asymptotically most powerfull under the local alternative models. The modified LRT is found is simulations to perform better than the C(a) test, the bootstrap test and Davies’ method. The empirical sampling study also reveals that the limiting distribution with some adjustment can satisfactorily approximate the quantiles of the test statistic even at a moderate sample size.

Keywords:

Asymptotic distribution , finite mixturem , genetic analysis , irregular model , strong identifiability.