{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T15:49:03Z","timestamp":1746805743647,"version":"3.40.5"},"reference-count":12,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"Science Foundation of Educational Committee of Jiangxi Province","award":["GJJ12388","20122BAB211007","2011GK2009","12BTJ014"],"award-info":[{"award-number":["GJJ12388","20122BAB211007","2011GK2009","12BTJ014"]}]},{"DOI":"10.13039\/501100004479","name":"Natural Science Foundation of Jiangxi Province","doi-asserted-by":"publisher","award":["GJJ12388","20122BAB211007","2011GK2009","12BTJ014"],"award-info":[{"award-number":["GJJ12388","20122BAB211007","2011GK2009","12BTJ014"]}],"id":[{"id":"10.13039\/501100004479","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science and Technology Projection of Hunan","award":["GJJ12388","20122BAB211007","2011GK2009","12BTJ014"],"award-info":[{"award-number":["GJJ12388","20122BAB211007","2011GK2009","12BTJ014"]}]},{"name":"National Social Science Foundation of China","award":["GJJ12388","20122BAB211007","2011GK2009","12BTJ014"],"award-info":[{"award-number":["GJJ12388","20122BAB211007","2011GK2009","12BTJ014"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>Under a balanced loss function, we derive the explicit formulae of the risk of the Stein-rule (SR) estimator, the positive-part Stein-rule (PSR) estimator, the feasible minimum mean squared error (FMMSE) estimator, and the adjusted feasible minimum mean squared error (AFMMSE) estimator in a linear regression model with multivariate<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>t<\/mml:mi><\/mml:mrow><\/mml:math>errors. The results show that the PSR estimator dominates the SR estimator under the balanced loss and multivariate<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mi>t<\/mml:mi><\/mml:mrow><\/mml:math>errors. Also, our numerical results show that these estimators dominate the ordinary least squares (OLS) estimator when the weight of precision of estimation is larger than about half, and vice versa. Furthermore, the AFMMSE estimator dominates the PSR estimator in certain occasions.<\/jats:p>","DOI":"10.1155\/2014\/129205","type":"journal-article","created":{"date-parts":[[2014,5,6]],"date-time":"2014-05-06T17:02:37Z","timestamp":1399395757000},"page":"1-7","source":"Crossref","is-referenced-by-count":1,"title":["Risk Comparison of Improved Estimators in a Linear Regression Model with Multivariate<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>t<\/mml:mi><\/mml:mrow><\/mml:math>Errors under Balanced Loss Function"],"prefix":"10.1155","volume":"2014","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8427-0515","authenticated-orcid":true,"given":"Guikai","family":"Hu","sequence":"first","affiliation":[{"name":"School of Mathematics and Econometrics, Hunan University, Changsha 410082, China"},{"name":"School of Science, East China Institute of Technology, Nanchang 330013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qingguo","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematics and Econometrics, Hunan University, Changsha 410082, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shenghua","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Economics and Trade, Hunan University, Changsha 410079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"issue":"354","key":"12","first-page":"400","volume":"71","year":"1976","journal-title":"Journal of the American Statistical Association"},{"first-page":"361","volume-title":"Estimation with quadratic loss","year":"1961","key":"5"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177697104"},{"key":"2","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1080\/00401706.1975.10489281","volume":"17","year":"1975","journal-title":"Technometrics"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1080\/03610929608831885"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(91)90026-A"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466602185033"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1007\/s00362-006-0321-z"},{"first-page":"377","volume-title":"Bayesian and non-Bayesian estimation using balanced loss functions","year":"1994","key":"13"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1080\/03610929608831878"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1080\/07474939708800376"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(98)00030-X"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/129205.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/129205.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/129205.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,22]],"date-time":"2017-06-22T08:47:30Z","timestamp":1498121250000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/129205\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":12,"alternative-id":["129205","129205"],"URL":"https:\/\/doi.org\/10.1155\/2014\/129205","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}