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| KANTOROVICH-TYPE INEQUALITIES AND THE MEASURES OF INEFFICIENCY OF THE GLSE | |
| 作者姓名： | 王松桂 杨虎 |
| 基金项目： | Project supported partially by the Third World Academy of Sciences under contract TWASRG 87-46 and by the National Natural Science Foundation |
| 摘 要： | In this paper we introduce some Kantorovich inequalities for the Euclidean norm of a matrix,that is, the upper bounds to ‖ (X'B~(-1)X)~(-1)X'B~(-1)AB~(-1)X (X'B~(-1)X)~(-1)A~(-1)X‖~2and to ‖(X'AX)~(-1)X'BX (X'AX)~(-1)X'CX‖~2 are given, where ‖A‖~2=trace(A'A). In terms of these inequalities the upperbounds to the three measures of inefficiency of the generalized least squares estimator (GLSE) ingeneral Gauss-Markov models are also established. |
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