| 约束型矩阵最小二乘估计预测 |
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| 引用本文： | 朱宁,严冠东,刘庆华.约束型矩阵最小二乘估计预测[J].汕头大学学报(自然科学版),2014(4):48-52. |
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| 作者姓名： | 朱宁 严冠东 刘庆华 |
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| 作者单位： | 桂林电子科技大学数学与计算科学学院,广西桂林541004 |
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| 摘 要： | 本文提出了约束型矩阵模型的最小二乘估计预测量,矩阵型MSE准则,矩阵型RT(·)准则,矩阵型MDE-准则.进一步,给出了约束型矩阵模型最小二乘估计预测关于MSE准则、RT(·)准则优于它的最佳线性无约束矩阵型最小二乘估计预测的充要条件.探究RT(·)准则与MDE-准则的相互转化关系,给出了约束型矩阵模型最小二乘估计预测优于无约束矩阵型最小二乘估计预测的充要条件.
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| 关 键 词： | 约束型矩阵预测量 无约束矩阵预测量 RT(·)准则 MDE-准则 最优性 |
Prediction of Least Squares Estimation on Constrained Matrix |
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| ZHU Ning,YAN Guandong,LIU Qinghua.Prediction of Least Squares Estimation on Constrained Matrix[J].Journal of Shantou University(Natural Science Edition),2014(4):48-52. |
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| Authors: | ZHU Ning YAN Guandong LIU Qinghua |
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| Institution: | (Mathematics and Computing Science College, Guilin University of Electronic Technology, Guilin 541004 Guangxi, China) |
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| Abstract: | The prediction of least squares estimation on constrained matrix, MSE criterion of matrix, RT（·） criterion of matrix and MDE criterion of matrix are presented in this paper. Further, the necessary and sufficient conditions are given when the prediction of least squares estimation on constrained matrix is less than the prediction of least squares estimation on unconstrained matrix about MSE criterion of matrix, or RT（· ） criterion of matrix. The relationship between MSE criterion and RT（·） criterion of matrix criterion is also studied. The necessary and sufficient conditions are given when prediction of least squares estimation on constrained matrix is less than the prediction of least squares estimation on unconstrained matrix about MDE-criterion of matrix criterion. |
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| Keywords: | prediction of constraint matrix prediction of unconstraint matrix criterion ofmatrix MDE-criteria of matrix optimality |
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