{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:39:55Z","timestamp":1753886395037,"version":"3.41.2"},"reference-count":22,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,8,31]],"date-time":"2006-08-31T00:00:00Z","timestamp":1156982400000},"content-version":"vor","delay-in-days":242,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>We investigate the empirical Bayes estimation problem of\nmultivariate regression coefficients under squared error loss\nfunction. In particular, we consider the regression model\n<jats:italic>Y<\/jats:italic> = <jats:italic>X<\/jats:italic><jats:italic>\u03b2<\/jats:italic> + <jats:italic>\u03b5<\/jats:italic>, where <jats:italic>Y<\/jats:italic> is an <jats:italic>m<\/jats:italic>\u2010vector of observations, <jats:italic>X<\/jats:italic> is a known <jats:italic>m<\/jats:italic> \u00d7 <jats:italic>k<\/jats:italic> matrix, <jats:italic>\u03b2<\/jats:italic> is an unknown <jats:italic>k<\/jats:italic>\u2010vector, and <jats:italic>\u03b5<\/jats:italic> is an <jats:italic>m<\/jats:italic>\u2010vector of unobservable random variables. The problem is squared error loss\nestimation of <jats:italic>\u03b2<\/jats:italic> based on some \u201cprevious\u201d data\n<jats:italic>Y<\/jats:italic><jats:sub>1<\/jats:sub>, \u2026, <jats:italic>Y<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub> as well as the \u201ccurrent\u201d data vector <jats:italic>Y<\/jats:italic> when <jats:italic>\u03b2<\/jats:italic> is distributed according to some unknown distribution\n<jats:italic>G<\/jats:italic>, where <jats:italic>Y<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub> satisfies <jats:italic>Y<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub> = <jats:italic>X<\/jats:italic><jats:italic>\u03b2<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub> + <jats:italic>\u03b5<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub>, <jats:italic>i<\/jats:italic> = 1, \u2026, <jats:italic>n<\/jats:italic>. We construct a new empirical Bayes estimator of\n<jats:italic>\u03b2<\/jats:italic> when <jats:italic>\u03b5<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub> ~ <jats:italic>N<\/jats:italic>(0, <jats:italic>\u03c3<\/jats:italic><jats:sup>2<\/jats:sup><jats:italic>I<\/jats:italic><jats:sub><jats:italic>m<\/jats:italic><\/jats:sub>), <jats:italic>i<\/jats:italic> = 1, \u2026, <jats:italic>n<\/jats:italic>. The performance of the proposed empirical Bayes\nestimator is measured using the mean squared error. The rates of\nconvergence of the mean squared error are obtained.<\/jats:p>","DOI":"10.1155\/ijmms\/2006\/51695","type":"journal-article","created":{"date-parts":[[2006,9,28]],"date-time":"2006-09-28T07:25:22Z","timestamp":1159428322000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On empirical Bayes estimation of multivariate regressioncoefficient"],"prefix":"10.1155","volume":"2006","author":[{"given":"R. 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