| 引用本文: | 胡庆军.先验信息下的改进主成分估计.[J].国防科技大学学报,1997,19(2):107-113.[点击复制] |
| Hu Qingjun.Improved Principal Components Estimate under Prior Information[J].Journal of National University of Defense Technology,1997,19(2):107-113[点击复制] |
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| 先验信息下的改进主成分估计 |
| 胡庆军 |
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(国防科技大学 系统工程与数学系 湖南 长沙 410073)
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| 摘要: |
| 对于线性模型Y = XC +ε, E(ε) = 0, Cov(ε,ε) =σ2I , 在先验信息(E(C) =0, Cov(C,C) =σ20I) 下, 本文给出主成分个数的一种更合理取法, 并提出了一种改进的主成分估计。文中证明了该估计是可容许估计, 且在“平均”均方误差意义下, 优于最小二乘估计, 亦优于主成分估计。 |
| 关键词: 线性模型, 先验信息, 改进主成分估计, 可容许性,“平均”均方误差 |
| DOI： |
| 投稿日期：1996-10-31 |
| 基金项目: |
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| Improved Principal Components Estimate under Prior Information |
| Hu Qingjun |
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(Department of Systems Engineering and Maths, NUDT, Changsha, 410073)
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| Abstract: |
| regard to the linear model Y = XC +ε, E(ε) = 0, Cov(ε,ε) =σ2I possessing the prior information: E(C) = 0, Cov(C, C) =σ20I, This article gives a best method of selecting the principal components' numbers in the principal components estimate and presents an improved principal components estimate. Theoretically, we prove that the improved estimate is admissible amd that it is marked much letter than Least Square Estimate and is better than the principal components estimate in a sense of “average”error of mean square. Simulation verifies the inference above. |
| Keywords: linear model, prior information, improved principal components estimate, admissible,“average”error of mean square. |
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