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Abstract: This paper develops a test for homogeneity in finite mixture models where themixing proportions are known a priori taken to be 0.5 and a common nuisanceparameter is present. Statistical tests based on the notion of ProjectedLikelihood Contrasts PLC are considered. The PLC is a slight modification ofthe usual likelihood ratio statistic or the Wilk-s $\Lambda$ and is similar inspirit to the Rao-s score test. Theoretical investigations have been carriedout to understand the large sample statistical properties of these tests.Simulation studies have been carried out to understand the behavior of the nulldistribution of the PLC statistic in the case of Gaussian mixtures with unknownmeans common variance as nuisance parameter and unknown variances commonmean as nuisance parameter. The results are in conformity with the theoreticalresults obtained. Power functions of these tests have been evaluated based onsimulations from Gaussian mixtures.



Author: Debapriya Sengupta, Rahul Mazumder

Source: https://arxiv.org/



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