{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T07:23:15Z","timestamp":1791444195821,"version":"4.3.3"},"reference-count":65,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"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":[[2026,2,13]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>Following Savage (1951)and Manski (2004), the literature on statistical treatment choice focuses on the mean of welfare regret. Ignoring other features of the regret distribution, however, can lead to a rule that is sensitive to sampling uncertainty. We propose to minimize the mean of a nonlinear transformation of regret and show that singleton rules are not essentially complete for nonlinear regret. Focusing on mean-square regret, we derive closed-form fractions for finite-sample Bayes and minimax optimal rules. Our approach is grounded in decision theory and extends to limit experiments. The treatment fractions can be viewed as the strength of evidence favouring treatment. We apply our framework to a normal regression model and sample-size calculations.<\/jats:p>","DOI":"10.1093\/biomet\/asag008","type":"journal-article","created":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T12:40:15Z","timestamp":1769776815000},"source":"Crossref","is-referenced-by-count":3,"title":["Treatment choice with nonlinear regret"],"prefix":"10.1093","volume":"113","author":[{"given":"Toru","family":"Kitagawa","sequence":"first","affiliation":[{"name":"Department of Economics, Brown University , Robinson Hall, 64 Waterman Street , Providence, Rhode Island 02912,","place":["U.S.A"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4080-7733","authenticated-orcid":false,"given":"Sokbae","family":"Lee","sequence":"additional","affiliation":[{"name":"Department of Economics, Columbia University , 420 West 118th Street , New York, New York 10027, \u00a0 sl3841@columbia.edu","place":["U.S.A."]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chen","family":"Qiu","sequence":"additional","affiliation":[{"name":"Department of Economics, Cornell University , 456 Uris Hall , Ithaca, New York 14853, \u00a0 cq62@cornell.edu","place":["U.S.A."]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,2,4]]},"reference":[{"key":"2026042200213668900_asag008-B1","author":"Adjaho","year":"2025"},{"key":"2026042200213668900_asag008-B2","doi-asserted-by":"crossref","first-page":"133","DOI":"10.3982\/ECTA15732","article-title":"Policy learning with observational data","volume":"89","author":"Athey","year":"2021","journal-title":"Econometrica"},{"key":"2026042200213668900_asag008-B3","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-4286-2","volume-title":"Statistical Decision Theory and Bayesian Analysis","author":"Berger","year":"1985"},{"key":"2026042200213668900_asag008-B4","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1016\/j.jeconom.2011.11.007","article-title":"Inferring welfare maximizing treatment assignment under budget constraints","volume":"167","author":"Bhattacharya","year":"2012","journal-title":"J. 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