方差分量模型中保G-M估计的线性变换

LINEAR TRANSFORMATIONS PRESERVING G-M ESTIMATOR IN A VARIANCE COMPONENTS MODEL

考虑方差分量模型（Ｙ，Ｘβ，ｔｉ＝１σ２ｉＶｉ），假设Ｘβ的Ｇ－Ｍ估计存在．本文给出了可观测的随机向量Ｙ的线性变换Ｆ为保Ｇ－Ｍ估计的变换（即存在ＦＹ的线性函数为Ｘβ的Ｇ－Ｍ估计）的充要条件，并指出在变换前后的模型中，Ｘβ的Ｇ－Ｍ估计相同．

Under a general variance components model {Y,Xβ,ti=1σ2iVi},a necessary and sufficient condition is established for a linear transformation,F,of the observable random vector Y to have the property that there exists a linear function of FY which is a G-M estimator of Xβ. A method for deriving a required G-M estimator from the transformed model {FY,FXβ,ti=1σ2iFViF′} is also indicated. These results are obtained under the condition of existence of G-M estimator for Xβ.