{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T07:30:25Z","timestamp":1791531025044,"version":"4.3.4"},"reference-count":18,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2006,7,19]],"date-time":"2006-07-19T00:00:00Z","timestamp":1153267200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2006,9,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>Since Stein's original proposal in 1962, a series of papers have constructed confidence regions of smaller volume than the standard spheres for the mean vector of a multivariate normal distribution. A general approach to this problem is developed here and used to calculate a lower bound on the attainable volume. Bayes and fiducial methods are involved in the calculation. Scheff\u00e9-type problems are used to show that low volume by itself does not guarantee favourable inferential properties.<\/jats:p>","DOI":"10.1111\/j.1467-9868.2006.00560.x","type":"journal-article","created":{"date-parts":[[2006,7,19]],"date-time":"2006-07-19T16:08:38Z","timestamp":1153325318000},"page":"655-670","source":"Crossref","is-referenced-by-count":17,"title":["Minimum Volume Confidence Regions for a Multivariate Normal Mean Vector"],"prefix":"10.1093","volume":"68","author":[{"given":"Bradley","family":"Efron","sequence":"first","affiliation":[{"name":"Stanford University , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2006,7,19]]},"reference":[{"key":"2023040708373590100_","volume-title":"Handbook of Mathematical Functions","author":"Abramowitz","year":"1968"},{"key":"2023040708373590100_","doi-asserted-by":"crossref","first-page":"716","DOI":"10.1214\/aos\/1176345068","article-title":"A robust generalized Bayes estimator and confidence region for a multivariate normal mean","volume":"8","author":"Berger","year":"1980","journal-title":"Ann. 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