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Abstract:
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In applications of mixture models, a typical approach is to assume the mixing distribution is discrete, and then to use AIC or BIC type of methods for model selection. In some applications, it is desirable to assume that the mixing distribution is continuous for better interpretability, or more importantly, for better estimation results. In this paper, we consider such a setting where each mixture component arises from the same distribution family that is parameterized in a location and dispersion parameter. We show a nesting property for some exponential family distributions, under which the mixture can be re-expressed as a new mixture, in which the components share a unified dispersion parameter while mixed in the location parameter. A cross-validation procedure for choice of the dispersion parameter is proposed in pair with NPMLE estimation of the mixing distribution.
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