{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T15:42:28Z","timestamp":1781538148935,"version":"3.54.5"},"reference-count":11,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,10,21]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>Asymptotically unbiased priors, introduced by Hartigan (1965), are designed to achieve second-order unbiasedness of Bayes estimators. This paper extends Hartigan\u2019s framework to non-independent-and-identically-distributed models by deriving a system of partial differential equations that characterizes asymptotically unbiased priors. Furthermore, we establish a necessary and sufficient condition for the existence of such priors and propose a simple procedure for constructing them. The proposed method is applied to the linear regression model and the nested error regression model (also known as the random effects model). Simulation studies evaluate the frequentist properties of the Bayes estimator under the asymptotically unbiased prior for the nested error regression model, highlighting its effectiveness in small-sample settings.<\/jats:p>","DOI":"10.1093\/biomet\/asaf068","type":"journal-article","created":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T12:12:59Z","timestamp":1759320779000},"source":"Crossref","is-referenced-by-count":1,"title":["Priors for second-order unbiased Bayes estimators"],"prefix":"10.1093","volume":"112","author":[{"given":"Mana","family":"Sakai","sequence":"first","affiliation":[{"name":"Graduate School of Economics, The University of Tokyo , 7-3-1 Hongo, Bunkyo-ku , Tokyo 113-0033, \u00a0 mana.sakai.77@gmail.com","place":["Japan"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Takeru","family":"Matsuda","sequence":"additional","affiliation":[{"name":"Graduate School of Information Science and Technology, The University of Tokyo , 7-3-1 Hongo, Bunkyo-ku , Tokyo 113-8656, \u00a0 matsuda@mist.i.u-tokyo.ac.jp","place":["Japan"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tatsuya","family":"Kubokawa","sequence":"additional","affiliation":[{"name":"Graduate School of Economics, The University of Tokyo , 7-3-1 Hongo, Bunkyo-ku , Tokyo 113-0033, \u00a0 tatsuya@e.u-tokyo.ac.jp","place":["Japan"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2025,10,6]]},"reference":[{"key":"2026032607100865500_asaf068-B1","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1093\/oso\/9780198522669.003.0003","volume-title":"Bayesian Statistics 4: Proceedings of the Fourth Valencia International Meeting, Dedicated to the memory of Morris H. 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