Predictive density estimation under the Wasserstein loss

Takeru Matsuda, William E. Strawderman

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)53-63
Number of pages11
JournalJournal of Statistical Planning and Inference
Volume210
DOIs
StatePublished - Jan 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Keywords

  • Optimal transport
  • Predictive density
  • Shrinkage estimation
  • Wasserstein distance

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