Bayesian inference and prediction for mean-mixtures of normal distributions. (English) Zbl 07731272

Summary: We study frequentist risk properties of predictive density estimators for mean mixtures of multivariate normal distributions, involving an unknown location parameter \(\theta \in \mathbf{R}^d\), and which include multivariate skew normal distributions. We provide explicit representations for Bayesian posterior and predictive densities, including the benchmark minimum risk equivariant (MRE) density, which is minimax and generalized Bayes with respect to an improper uniform density for \(\theta\). For four dimensions or more, we obtain Bayesian densities that improve uniformly on the MRE density under Kullback-Leibler loss. We also provide plug-in type improvements, investigate implications for certain type of parametric restrictions on \(\theta\), and illustrate and comment the findings based on numerical evaluations.


62C20 Minimax procedures in statistical decision theory
62C25 Compound decision problems in statistical decision theory
62C10 Bayesian problems; characterization of Bayes procedures
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