{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,23]],"date-time":"2026-07-23T12:37:50Z","timestamp":1784810270301,"version":"3.55.0"},"reference-count":31,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,8,25]],"date-time":"2020-08-25T00:00:00Z","timestamp":1598313600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We propose probability and density forecast combination methods that are defined using the entropy regularized Wasserstein distance. First, we provide a theoretical characterization of the combined density forecast based on the regularized Wasserstein distance under the assumption. More specifically, we show that the regularized Wasserstein barycenter between multivariate Gaussian input densities is multivariate Gaussian, and provide a simple way to compute mean and its variance\u2013covariance matrix. Second, we show how this type of regularization can improve the predictive power of the resulting combined density. Third, we provide a method for choosing the tuning parameter that governs the strength of regularization. Lastly, we apply our proposed method to the U.S. inflation rate density forecasting, and illustrate how the entropy regularization can improve the quality of predictive density relative to its unregularized counterpart.<\/jats:p>","DOI":"10.3390\/e22090929","type":"journal-article","created":{"date-parts":[[2020,8,25]],"date-time":"2020-08-25T09:30:07Z","timestamp":1598347807000},"page":"929","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Probability Forecast Combination via Entropy Regularized Wasserstein Distance"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5708-7627","authenticated-orcid":false,"given":"Ryan","family":"Cumings-Menon","sequence":"first","affiliation":[{"name":"The US Census Bureau, 4600 Silver Hill Rd, Suitland-Silver Hill, MD 20746, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Minchul","family":"Shin","sequence":"additional","affiliation":[{"name":"Federal Reserve Bank of Philadelphia, Ten Independence Mall, Philadelphia, PA 19106, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,8,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1016\/j.jeconom.2011.02.017","article-title":"Optimal prediction pools","volume":"164","author":"Geweke","year":"2011","journal-title":"J. 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