| 分块奇异线性模型及其导出的奇异线性模型间的最小范数二次无偏估计等价性研究 |
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| 引用本文： | 张宝学,鹿长余.分块奇异线性模型及其导出的奇异线性模型间的最小范数二次无偏估计等价性研究[J].应用概率统计,2004,20(4):393-403. |
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| 作者姓名： | 张宝学 鹿长余 |
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| 作者单位： | 1. 北京理工大学数学系,北京,100081;复旦大学数学研究所,上海,200433
2. 华东师范大学统计系,上海,200062 |
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| 基金项目： | TheprojectwassupportedbyChinaMathematicsTianYuanYouthFoundation(10226024)
scientificresearchfoundationofBeijingInstituteofTechnologyandChinaPostdoctoralScienceFoundation.TheworkwassupportedinpartbytheNationalNaturalScienceFoundation(10071011)ofChina. |
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| 摘 要： | 本文考虑一般线性模型A=(y,X1β1 X2β2,σ^2V)及其导出线性模型，其中V是已知的非负定矩阵，X=(X1：X2)是已知的设计矩阵，给出了线性模型A及其导出线性模型间最小范数二次无偏估计间差的表达式，更进一步，建立了线性模型A及其导出线性模型间最小范数二次无偏估计相等的充分必要条件。
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| 关 键 词： | 奇异线性模型 最小范数二次无偏估计 投影 |
A Study of the Equivalence of the MINQUEs between a Partitioned Singular Linear Model and Its Reduced Singular Linear Models |
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| Abstract.A Study of the Equivalence of the MINQUEs between a Partitioned Singular Linear Model and Its Reduced Singular Linear Models[J].Chinese Journal of Applied Probability and Statisties,2004,20(4):393-403. |
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| Authors: | Abstract |
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| Abstract: | In this article we consider the general linear regression model A = (y,X1β1 + X2β2,σ2V) and its four reduced linear models, where V is known nonnegative definite and X = (X1: X2) can be rank-deficient. The formulae for the differences between the Minimum Norm Quadratic Unbiased Estimators (MINQUEs) of σ2under the model A and its MINQUEs under reduced linear models of A are given. Further, the necessary and sufficient conditions for the equalities between the MINQUEs of σ2 under A and its reduced linear models are established. |
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| Keywords: | Singular linear model MINQUEs projector |
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