{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:28:01Z","timestamp":1760243281385,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2014,5,28]],"date-time":"2014-05-28T00:00:00Z","timestamp":1401235200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We investigate the asymptotic construction of constant-risk Bayesian predictive densities under the Kullback\u2013Leibler risk when the distributions of data and target variables are different and have a common unknown parameter. It is known that the Kullback\u2013Leibler risk is asymptotically equal to a trace of the product of two matrices: the inverse of the Fisher information matrix for the data and the Fisher information matrix for the target variables. We assume that the trace has a unique maximum point with respect to the parameter. We construct asymptotically constant-risk Bayesian predictive densities using a prior depending on the sample size. Further, we apply the theory to the subminimax estimator problem and the prediction based on the binary regression model.<\/jats:p>","DOI":"10.3390\/e16063026","type":"journal-article","created":{"date-parts":[[2014,5,28]],"date-time":"2014-05-28T11:10:36Z","timestamp":1401275436000},"page":"3026-3048","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Asymptotically Constant-Risk Predictive Densities When the Distributions of Data and Target Variables Are Different"],"prefix":"10.3390","volume":"16","author":[{"given":"Keisuke","family":"Yano","sequence":"first","affiliation":[{"name":"Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fumiyasu","family":"Komaki","sequence":"additional","affiliation":[{"name":"Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan"},{"name":"RIKEN Brain Science Institute, 2-1 Hirosawa, Wako City, Saitama 351-0198, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2014,5,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1093\/biomet\/62.3.547","article-title":"Goodness of prediction fit","volume":"62","author":"Aitchison","year":"1975","journal-title":"Biometrika"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1093\/biomet\/83.2.299","article-title":"On asymptotic properties of predictive distributions","volume":"83","author":"Komaki","year":"1996","journal-title":"Biometrika"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2083","DOI":"10.1214\/aos\/1024691462","article-title":"The maximum likelihood prior","volume":"26","author":"Hartigan","year":"1998","journal-title":"Ann. 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