{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:31Z","timestamp":1740134551425,"version":"3.37.3"},"reference-count":23,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11171361","20110191110033"],"award-info":[{"award-number":["11171361","20110191110033"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002338","name":"Ministry of Education of China","doi-asserted-by":"crossref","award":["11171361","20110191110033"],"award-info":[{"award-number":["11171361","20110191110033"]}],"id":[{"id":"10.13039\/501100002338","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>We introduce the weighted mixed almost unbiased ridge estimator (WMAURE) based on the weighted mixed estimator (WME) (Trenkler and Toutenburg 1990) and the almost unbiased ridge estimator (AURE) (Akdeniz and Erol 2003) in linear regression model. We discuss superiorities of the new estimator under the quadratic bias (QB) and the mean square error matrix (MSEM) criteria. Additionally, we give a method about how to obtain the optimal values of parameters<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>k<\/mml:mi><\/mml:mrow><\/mml:math>and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mn>w<\/mml:mn><\/mml:mrow><\/mml:math>. Finally, theoretical results are illustrated by a real data example and a Monte Carlo study.<\/jats:p>","DOI":"10.1155\/2013\/902715","type":"journal-article","created":{"date-parts":[[2013,5,1]],"date-time":"2013-05-01T21:24:12Z","timestamp":1367443452000},"page":"1-10","source":"Crossref","is-referenced-by-count":3,"title":["On the Weighted Mixed Almost Unbiased Ridge Estimator in Stochastic Restricted Linear Regression"],"prefix":"10.1155","volume":"2013","author":[{"given":"Chaolin","family":"Liu","sequence":"first","affiliation":[{"name":"College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hu","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jibo","family":"Wu","sequence":"additional","affiliation":[{"name":"College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1965.10480787"},{"issue":"1","key":"2","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1080\/00401706.1970.10488634","volume":"12","year":"1970","journal-title":"Technometrics"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1080\/03610928408828675"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1080\/03610929308831034"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1081\/STA-100108454"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/0165-1765(84)90178-2"},{"issue":"3","key":"7","first-page":"342","volume":"48","year":"1986","journal-title":"Sankhy\u0101 B"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1080\/03610929508831585"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1081\/STA-120025385"},{"issue":"264","key":"10","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1080\/01621459.1953.10501201","volume":"48","year":"1953","journal-title":"Journal of the American Statistical Association"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.2307\/2525589"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1963.10500854"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1007\/s00362-006-0300-4"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1007\/s00362-007-0102-3"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1007\/s00362-008-0169-5"},{"key":"16","first-page":"735","volume":"70","year":"1990","journal-title":"Zeitschrift f\u00fcr Angewandte Mathematik und Mechanik"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1080\/02331880903573153"},{"year":"2008","key":"18"},{"issue":"3","key":"19","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1111\/j.2517-6161.1976.tb01588.x","volume":"38","year":"1976","journal-title":"Journal of the Royal Statistical Society B"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1007\/BF02924687"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1021\/ie50275a002"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1081\/STA-120019959"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1080\/03610926.2010.505693"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/902715.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/902715.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/902715.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,9]],"date-time":"2024-05-09T23:06:02Z","timestamp":1715295962000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/902715\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":23,"alternative-id":["902715","902715"],"URL":"https:\/\/doi.org\/10.1155\/2013\/902715","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2013]]}}}