Predictive density estimation under the Wasserstein loss

Takeru Matsuda; William E. Strawderman

doi:10.1016/j.jspi.2020.05.005

Predictive density estimation under the Wasserstein loss

Takeru Matsuda, William E. Strawderman

School of Arts and Sciences, Statistics

Research output: Contribution to journal › Article › peer-review

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)
Pages (from-to)	53-63
Number of pages	11
Journal	Journal of Statistical Planning and Inference
Volume	210
DOIs	https://doi.org/10.1016/j.jspi.2020.05.005
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

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title = "Predictive density estimation under the Wasserstein loss",

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.",

keywords = "Optimal transport, Predictive density, Shrinkage estimation, Wasserstein distance",

author = "Takeru Matsuda and Strawderman, {William E.}",

note = "Funding Information: The authors are grateful to the referees for valuable comments. This work was supported by JSPS KAKENHI, Japan Grant Numbers 17H06569 and 19K20220 . William Strawderman{\textquoteright}s research is partially supported by a grant from the Simons Foundation, USA ( #418098 ).",

year = "2021",

month = jan,

doi = "10.1016/j.jspi.2020.05.005",

language = "English (US)",

volume = "210",

pages = "53--63",

journal = "Journal of Statistical Planning and Inference",

issn = "0378-3758",

publisher = "Elsevier",

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T1 - Predictive density estimation under the Wasserstein loss

AU - Matsuda, Takeru

AU - Strawderman, William E.

N1 - Funding Information: The authors are grateful to the referees for valuable comments. This work was supported by JSPS KAKENHI, Japan Grant Numbers 17H06569 and 19K20220 . William Strawderman’s research is partially supported by a grant from the Simons Foundation, USA ( #418098 ).

PY - 2021/1

Y1 - 2021/1

N2 - 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.

AB - 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.

KW - Optimal transport

KW - Predictive density

KW - Shrinkage estimation

KW - Wasserstein distance

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