Abstract
We investigate predictive density estimation under the L2 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. Simulation results are also presented.
Original language | English (US) |
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Pages (from-to) | 53-63 |
Number of pages | 11 |
Journal | Journal of Statistical Planning and Inference |
Volume | 210 |
DOIs | |
State | Published - Jan 2021 |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics
Keywords
- Optimal transport
- Predictive density
- Shrinkage estimation
- Wasserstein distance