{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,19]],"date-time":"2026-10-19T15:42:49Z","timestamp":1792424569314,"version":"4.5.0"},"reference-count":0,"publisher":"Oxford University Press (OUP)","license":[{"start":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T00:00:00Z","timestamp":1792022400000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>We show that for any concave utility, the expected utility of an e-variable can only increase after conditioning on a sufficient statistic, echoing the classic Rao-Blackwell theorem. The simplest form of the result has a straightforward proof using Jensen\u2019s inequality, but we prove more sophisticated versions. We provide several applications of this insight, including a derivation of the log-optimal e-variable for testing the variance in a linear regression model.<\/jats:p>","DOI":"10.1093\/biomet\/asag061","type":"journal-article","created":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T11:52:00Z","timestamp":1792065120000},"source":"Crossref","is-referenced-by-count":0,"title":["Rao-Blackwellized e-variables"],"prefix":"10.1093","author":[{"given":"D","family":"de Roos","sequence":"first","affiliation":[{"name":"Machine Learning Group, Centrum Wiskunde & Informatica , Science Park 123, 1098 XG, Amsterdam, The","place":["Netherlands"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"B","family":"Chugg","sequence":"additional","affiliation":[{"name":"Carnegie Mellon University Departments of Statistics and Machine Learning, , 5000 Forbes Avenue, Pittsburgh, Pennsylvania 15213, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"P","family":"Gr\u00fcnwald","sequence":"additional","affiliation":[{"name":"Machine Learning Group, Centrum Wiskunde & Informatica , Science Park 123, 1098 XG, Amsterdam, The","place":["Netherlands"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A","family":"Ramdas","sequence":"additional","affiliation":[{"name":"Stanford University Department of Statistics, , 390 Jane Stanford Way, Stanford, California 94305, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,10,15]]},"container-title":["Biometrika"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/biomet\/advance-article-pdf\/doi\/10.1093\/biomet\/asag061\/71964154\/asag061.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biomet\/advance-article-pdf\/doi\/10.1093\/biomet\/asag061\/71964154\/asag061.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,19]],"date-time":"2026-10-19T15:26:50Z","timestamp":1792423610000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/biomet\/advance-article\/doi\/10.1093\/biomet\/asag061\/8917306"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10,15]]},"references-count":0,"URL":"https:\/\/doi.org\/10.1093\/biomet\/asag061","relation":{},"ISSN":["0006-3444","1464-3510"],"issn-type":[{"value":"0006-3444","type":"print"},{"value":"1464-3510","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,10,15]]},"article-number":"asag061"}}