| 设计阵列亏秩时几种估计性能的比较 |
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| 引用本文： | 刘谢进,朱允民.设计阵列亏秩时几种估计性能的比较[J].四川大学学报(自然科学版),2002,39(5):839-842. |
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| 作者姓名： | 刘谢进 朱允民 |
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| 作者单位： | 1. 淮南师范学院数学系,安徽,淮南,232001;四川大学数学学院,成都,610064
2. 四川大学数学学院,成都,610064 |
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| 摘 要： | 在给定的线性模型下，讨论了在设计阵列亏秩时，最小二乘估计、最优加权最小二乘估计和线性无偏最小方差估计的性能比较。得出了在一定条件下，最优加权最小二乘估计等价于线性无偏最小方差估计。在噪声方差矩阵可逆、未知参数方差矩阵可逆条件下，可算出最优加权最小二乘估计与线性无偏最小方差估计方差的差表达式，并在一定条件下，两者趋于一致。
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| 关 键 词： | 阵列亏秩 线性模型 最小二乘估计 最优加权最小二乘估计 线性无偏最小方差估计 性能比较 |
| 文章编号： | 0490-6756(2002)05-0839-04 |
The Performance Comparison of Several Estimate in the Condition of Singular Matrix |
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| LIU Xie-jin ,ZHU Yun-min.The Performance Comparison of Several Estimate in the Condition of Singular Matrix[J].Journal of Sichuan University (Natural Science Edition),2002,39(5):839-842. |
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| Authors: | LIU Xie-jin ZHU Yun-min |
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| Institution: | LIU Xie-jin 1,2,ZHU Yun-min 2 |
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| Abstract: | The discussion on the performance coparison among least squares estimate, optimally weighted least squares estimate and linear unbiased minimum variance estimate of column singular design matrix for a linear model is presented. Under a condition on noise variance matrix invertibility and unknown parameter variance matrix invertilibity, the difference between optimally weighted least squares estimate and linear unbiased minimum variance estimate error variances can be calculated, and the two estimates can converge to the same one under a certain condition. |
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| Keywords: | linear model least squares optimally weighted least squares linear unbiased minimum variance estimate |
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