Finite mixture models and their applications

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Finite mixture models are widely applied to data sets in which several homogeneous populations are mixed together. In financial economics, mixtures of three normal distributions are often applied to daily stock returns due to the existence of three risk regimes: low, normal and high. The number of homogeneous populations in a finite mixture is of great interest in applications. For example in statistical genetics, this number reflects the number of major genes in action. In the first project, a novel and practically convenient method, called the EM-test, will be developed for testing the number of homogeneous populations in a finite mixture.