## A modified likelihood ratio test for homogeneity in finite mixture models.(English)Zbl 0976.62011

Summary: Testing for homogeneity in finite mixture models has been investigated by many researchers. The asymptotic null distribution of the likelihood ratio test (LRT) is very complex and difficult to use in practice. We propose a modified LRT for homogeneity in finite mixture models with a general parametric kernel distribution family. The modified LRT has a $$\chi^2$$-type of null limiting distribution and is asymptotically most powerful under local alternatives. Simulations show that it performs better than competing tests. They also reveal that the limiting distribution with some adjustment can satisfactorily approximate the quantiles of the test statistic, even for moderate sample sizes.

### MSC:

 62F03 Parametric hypothesis testing 62E20 Asymptotic distribution theory in statistics
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