Abstract:
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In biomedical studies, testing for homogeneity between two groups where one group is modeled by parametric mixture models is often of interest. In this study, we use a semiparametric exponential family mixture model where the distribution function for the reference group is unspecified. By allowing Box-Cox transformations, the model extends the exponential family mixture model and offers more flexibility to characterize the heterogeneity. We construct a novel score test to test the homogeneity between two groups. To address the technical challenges due to irregularities of the mixture model, we propose a modification of the score test, so that the resulting test enjoys the Wilks phenomenon. We show the finite-sample most powerful property and asymptotic power function of the proposed test. The proposed test is evaluated by simulation studies and applied to a DNA methylation data set.
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