{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T03:13:08Z","timestamp":1761621188855},"reference-count":38,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,10,2]],"date-time":"2014-10-02T00:00:00Z","timestamp":1412208000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2015,8]]},"abstract":"<jats:p>This paper is an extension of Magnus (2002,<jats:italic>Econometrics Journal<\/jats:italic>5, 225\u2013236) to multiple dimensions. We consider estimation of a multivariate normal mean under sum of squared error loss. We construct the efficiency bound (the lowest achievable risk) for minimax shrinkage estimation in the class of minimax orthogonally invariate estimators satisfying the sufficient conditions of Efron and Morris (1976,<jats:italic>Annals of Statistics<\/jats:italic>4, 11\u201321). This allows us to compare the regret of existing orthogonally invariate shrinkage estimators. We also construct a new shrinkage estimator which achieves substantially lower maximum regret than existing estimators.<\/jats:p>","DOI":"10.1017\/s0266466614000693","type":"journal-article","created":{"date-parts":[[2014,10,2]],"date-time":"2014-10-02T10:33:24Z","timestamp":1412246004000},"page":"860-879","source":"Crossref","is-referenced-by-count":8,"title":["SHRINKAGE EFFICIENCY BOUNDS"],"prefix":"10.1017","volume":"31","author":[{"given":"Bruce E.","family":"Hansen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,10,2]]},"reference":[{"key":"S0266466614000693_ref11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S0266466608090099","article-title":"Lasso-type GMM estimator","volume":"25","author":"Caner","year":"2009","journal-title":"Econometric Theory"},{"key":"S0266466614000693_ref26","article-title":"Automated estimation of vector error correction models","author":"Liao","year":"2014","journal-title":"Econometric Theory"},{"key":"S0266466614000693_ref28","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-11761-3","volume-title":"Formulas and Theorems for the Special Functions of Mathematical Physics","author":"Magnus","year":"1966"},{"key":"S0266466614000693_ref19","first-page":"361","article-title":"Estimation with quadratic loss","volume":"1","author":"James","year":"1961","journal-title":"Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability"},{"key":"S0266466614000693_ref27","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1111\/1368-423X.t01-1-00082","article-title":"Estimation of the mean of a univariate normal distribution with known variance","volume":"5","author":"Magnus","year":"2002","journal-title":"Econometrics Journal"},{"key":"S0266466614000693_ref24","doi-asserted-by":"crossref","first-page":"2249","DOI":"10.1080\/03610928208828386","article-title":"Generalized James-Stein estimators","volume":"11","author":"Li","year":"1982","journal-title":"Communications in Statistics - 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