Fundamental Equations of BLUE and BLUP in the Multivariate Linear Model with Applications |
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| Authors: | Yonghui Liu Chenqi Xia |
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| Institution: | 1. Department of Applied Mathematics , Shanghai Finance University , Shanghai , China Liuyh@lsec.cc.ac.cn;3. Department of Applied Mathematics , Shanghai University of Finance and Economics , Shanghai , China |
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| Abstract: | Ordinary least squares estimator (OLSE), best linear unbiased estimator (BLUE), and best linear unbiased predictor (BLUP) in the general linear model with new observations are generalized to the general multivariate linear model. The fundamental equations of BLUE and BLUP in the multivariate linear model are derived by two methods, including the vectorization method and projection method. By using the matrix rank method, some new results of linear BLUE-sufficiency, linear BLUP-sufficiency, and the equality of OLSE, BLUE, and BLUP are given in the multivariate linear model. |
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| Keywords: | BLUE BLUP Linear BLUE-sufficiency Linear BLUP-sufficiency Multivariate linear model Matrix rank method OLSE Projection method Vectorization method |
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