Characterization of Admissible Linear Estimators in Multivariate Linear Model with Respect to Inequality Constraints under Matrix Loss Function |
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| Authors: | Shangli Zhang Zhide Fang Gang Liu |
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| Institution: | 1. School of Science , Beijing Jiaotong University , Beijing , China;2. State Key Laboratory of Rail Traffic Control and Safety , Beijing Jiaotong University , Beijing , China shlzhang@bjtu.edu.cn;4. Biostatistics Section, School of Public Health , LSU Health Sciences Center , New Orleans , Louisiana , USA;5. School of Information , Renming University , Beijing , China |
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| Abstract: | In this article, we study the characterization of admissible linear estimators in a multivariate linear model with inequality constraint, under a matrix loss function. In the homogeneous class, we present several equivalent, necessary and sufficient conditions for a linear estimator of estimable functions to be admissible. In the inhomogeneous class, we find that the necessary and sufficient conditions depend on the rank of the matrix in the constraint. When the rank is greater than one, the necessary and sufficient conditions are obtained. When the rank is equal to one, we have necessary conditions and sufficient conditions separately. We also obtain the necessary and sufficient conditions for a linear estimator of inestimable function to be admissible in both classes. |
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| Keywords: | Admissibility Homogeneous/Inhomogeneous linear estimation Inequality constraints Matrix loss Multivariate linear model |
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