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Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Admissible Estimators in the General Multivariate Linear Model with Respect to Inequality | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 718927 12 pages doi 10.1155 2009 718927 Research Article Admissible Estimators in the General Multivariate Linear Model with Respect to Inequality Restricted Parameter Set Shangli Zhang 1 Gang Liu 2 and Wenhao Gui3 1 School of Science Beijing Jiaotong University Beijing 100044 China 2 School of Information Renmin University of China Beijing 100872 China 3 Department of Statistics Florida State University Tallahassee FL 32306 USA Correspondence should be addressed to Wenhao Gui wenhao@stat.fsu.edu Received 28 May 2009 Accepted 11 August 2009 Recommended by Kunquan Lan By using the methods of linear algebra and matrix inequality theory we obtain the characterization of admissible estimators in the general multivariate linear model with respect to inequality restricted parameter set. In the classes of homogeneous and general linear estimators the necessary and suffcient conditions that the estimators of regression coeffcient function are admissible are established. Copyright 2009 Shangli Zhang et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction Throughout this paper Rmxn Rm and Rm denote the set of m X n real matrices the subset of Rmxm consisting of symmetric matrices and the subset of Rm consisting of nonnegative definite matrices respectively. The symbols A ji A A A- and tr A stand for the transpose the range Moore-Penrose inverse generalized inverse and trace of A e Rmxn respectively. For any A B e Rm A B means A - B 0. Consider the general multivariate linear model with respect to inequality restricted parameter set Y XB 0 s V 1.1 B - Bo X NX B - Bo s 2 Journal of Inequalities and Applications where Y e Rnxq is an observable random matrix X e Rnxp Bo Rpxq V e Rn and N e R are known matrices
