Predictive density estimation under the Wasserstein loss

04/05/2019

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by   Takeru Matsuda, et al.

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We investigate predictive density estimation under the L^2 Wasserstein loss for location families and location-scale families. We show that plug-in densities form a complete class and that the Bayesian predictive density is given by the plug-in density with the posterior mean of the location and scale parameters. We provide Bayesian predictive densities that dominate the best equivariant one in normal models.