Discrete mixture representations of parametric distribution families: geometry and statistics
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We investigate existence and properties of discrete mixture representations P_θ =∑_i∈ E w_θ(i) Q_i for a given family P_θ, θ∈Θ, of probability measures. The noncentral chi-squared distributions provide a classical example. We obtain existence results and results about geometric and statistical aspects of the problem, the latter including loss of Fisher information, Rao-Blackwellization, asymptotic efficiency and nonparametric maximum likelihood estimation of the mixing probabilities.
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