| 多元线性模型回归系数的Stein型估计 |
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| 引用本文： | 陈世基.多元线性模型回归系数的Stein型估计[J].福建师范大学学报(自然科学版),1991,7(1):7-13. |
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| 作者姓名： | 陈世基 |
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| 作者单位： | 福建师范大学数学系 |
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| 摘 要： | 本文对多元线性模型的回归系数提出了Stein型估计,可使其MSE小于LS估计。分析了选取参数矩阵K的MSE准则存在的缺陷,于是应用Q(C)准则克服这些缺陷。从理论上证明了Q(C)准则的优良性,并给出了确定C的方法。
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| 关 键 词： | 多元线性模型 Stein估计 回归系数 |
Stein Estimator of Regression Coefficients in the Multivariate Linear Model |
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| Chen Shiji.Stein Estimator of Regression Coefficients in the Multivariate Linear Model[J].Journal of Fujian Teachers University(Natural Science),1991,7(1):7-13. |
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| Authors: | Chen Shiji |
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| Institution: | Department of Mathematics |
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| Abstract: | In this paper a Stein estimator is considered. Through choosing the matrix K, we prove that the Stein estimator has more precision than LSE. It is also pointed out in this paper the criterion MSE for choosing the matrix K has several weaknesses. In order to overcome these weaknesses, the criteria Q(C) is applied to choosing the matrix K, it in cludes the criterion MSE as a special case. The good properties of criteria Q(C) are proved and discussed from theoretical point of view. The methods of determining C for pratical use are suggested |
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| Keywords: | least square estimate mean square error admissible estimate mean square residual criteria Q(C) |
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