{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T15:01:51Z","timestamp":1746802911702,"version":"3.40.5"},"reference-count":19,"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":"Scientific Research Foundation of Chongqing University of Arts and Sciences","award":["R2013SC12","11201505","KJTD201321"],"award-info":[{"award-number":["R2013SC12","11201505","KJTD201321"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["R2013SC12","11201505","KJTD201321"],"award-info":[{"award-number":["R2013SC12","11201505","KJTD201321"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013084","name":"Program for Innovation Team Building at Institutions of Higher Education in Chongqing","doi-asserted-by":"crossref","award":["R2013SC12","11201505","KJTD201321"],"award-info":[{"award-number":["R2013SC12","11201505","KJTD201321"]}],"id":[{"id":"10.13039\/501100013084","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>The stochastic restricted<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mi>r<\/mml:mi><mml:mtext>-<\/mml:mtext><mml:mi>k<\/mml:mi><\/mml:math>class estimator and stochastic restricted<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mi>r<\/mml:mi><mml:mtext>-<\/mml:mtext><mml:mi>d<\/mml:mi><\/mml:math>class estimator are proposed for the vector of parameters in a multiple linear regression model with stochastic linear restrictions. The mean squared error matrix of the proposed estimators is derived and compared, and some properties of the proposed estimators are also discussed. Finally, a numerical example is given to show some of the theoretical results.<\/jats:p>","DOI":"10.1155\/2014\/173836","type":"journal-article","created":{"date-parts":[[2014,1,2]],"date-time":"2014-01-02T21:02:12Z","timestamp":1388696532000},"page":"1-6","source":"Crossref","is-referenced-by-count":3,"title":["On the Stochastic Restricted<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mi>r<\/mml:mi><mml:mtext>-<\/mml:mtext><mml:mi>k<\/mml:mi><\/mml:math>Class Estimator and Stochastic Restricted<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mi>r<\/mml:mi><mml:mtext>-<\/mml:mtext><mml:mi>d<\/mml:mi><\/mml:math>Class Estimator in Linear Regression Model"],"prefix":"10.1155","volume":"2014","author":[{"given":"Jibo","family":"Wu","sequence":"first","affiliation":[{"name":"School of Mathematics and Finances, Chongqing University of Arts and Sciences, Chongqing 402160, China"},{"name":"Department of Mathematics and KLDAIP, Chongqing University of Arts and Sciences, Chongqing 402160, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"13","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1965.10480787"},{"issue":"1","key":"8","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1080\/00401706.1970.10488634","volume":"12","year":"1970","journal-title":"Technometrics"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1080\/03610928408828675"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1080\/03610929308831027"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1081\/STA-100108454"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1080\/03610926.2011.577552"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1155\/2013\/858794"},{"year":"1995","series-title":"Springer Series in Statistics","key":"14"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1953.10501201"},{"issue":"1","key":"15","doi-asserted-by":"crossref","first-page":"65","DOI":"10.2307\/2525589","volume":"2","year":"1961","journal-title":"International Economic Review"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1963.10500854"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1007\/s00362-008-0169-5"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1007\/s00362-006-0300-4"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1155\/2013\/902715"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1080\/00949650903471023"},{"issue":"1-2","key":"3","first-page":"5","volume":"31","year":"1983","journal-title":"Bulletin of the Polish Academy of Sciences: Mathematics"},{"year":"2006","key":"17"},{"volume":"156","year":"1998","series-title":"Statistics: Textbooks and Monographs","key":"6"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1081\/STA-120025385"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/173836.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/173836.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/173836.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,11]],"date-time":"2020-05-11T18:03:32Z","timestamp":1589220212000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/173836\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":19,"alternative-id":["173836","173836"],"URL":"https:\/\/doi.org\/10.1155\/2014\/173836","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}