Predictive density estimation under the Wasserstein loss

Abstract

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.

References in corpus (2)

• Improved minimax predictive densities under Kullback--Leibler loss
• Admissible predictive density estimation

Cited by in corpus (2)

• Bayesian Predictive Density Estimation for a Chi-squared Model Using Information from a Normal Observation with Unknown Mean and Variance
• Wasserstein Statistics in One-dimensional Location-Scale Model