Test of Homogeneity

Abstract

The quest for effective tests of homogeneity within mixture models has a long history. An illustrative example provided by Hartigan shows that the likelihood ratio statistic, unlike its counterpart in regular models, tends to diverge to infinity even in the context of an extremely simplified normal mixture model. While imposing compact restrictions on the subpopulation parameter space and a separation condition can prevent this divergence and land on a limiting distribution, it does not lead to a practical testing procedure. In contrast, the C($\alpha$) test, which is a modification of the popular score test, exhibits a simple limiting distribution and proves to be an effective tool for homogeneity testing in mixture models with single-parameter subpopulation distributions. Chapter 9 is dedicated to introducing the C($\alpha$) test and providing specific expressions for its application within NEF-VEF mixtures.