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Abstract:
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Most existing methods in the literature for testing of homogeneity, explicitly or implicitly, are derived under the condition of finite Fisher information and a compactness assumption on the space of the mixing parameters. The finite Fisher information condition can prevent their usage to many important mixture models, such as the mixture of geometric distributions, exponential distributions and more generally mixture models in scale distribution families. The compactness assumption is relatively harmless, yet it can be awkward to specify a compact region for the mixing parameters in applications. In this presentation, we introduce an EM-test, which is shown to be free of all these shortcomings and have very simple limiting distributions. Current results indicate that this method has the potential to be generally applicable.
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