摘要
本文考虑一般线性模型A=(y,X1β1+X2β2,σ2V)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.
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 σ2 under 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,
出处
《应用概率统计》
CSCD
北大核心
2004年第4期393-403,共11页
Chinese Journal of Applied Probability and Statistics
基金
TheprojectwassupportedbyChinaMathematicsTianYuanYouthFoundation(10226024)scientificresearchfoundationofBeijingInstituteofTechnologyandChinaPostdoctoralScienceFoundation.TheworkwassupportedinpartbytheNationalNaturalScienceFoundation(10071011)ofChina.
