Bayesian inference and prediction for mean-mixtures of normal distributions

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