摘要
在一般Ｇａｕｓｓ－Ｍａｒｋｏｆｆ模型｛Ｙ，Ｘβ，Ｖ｝下，设Ｆ是一个适当阶矩阵，Ｃ为任意适当维向量，本文找到了ＡＹ是Ｃ＇β的最小偏倚估计的充分必要条件及ＡＹ是Ｃ＇β的最佳线性最小偏倚估计的充要条件．在以概率１意义下，证明了对于所有适当维向量Ｃ，Ｃ＇β的最佳线性最小偏倚估计能被表示成ＦＹ的线性函数的充要条件，且在此条件下，线性变换保最佳线性最小偏倚估计．
Under a general Gauss-Markoff model {Y,Xβ,V} , Let F be a matrix of appropriate order and C be an arbitrary vector of appropriate order. Two necessary and sufficient conditions are established for AY to be minimum bias estimators of C'β and AY to be best linear minimum bias estimators of C'β. With probability 1, a necessary and sufficient condition is established for a linear transformation F of Y to have the property that there exists a linear function of FY which is a best linear minimum bias estimator of C'β for all vectors C of appropriate order. We also demonstrate that the linear transformation preserves best linear minimum bias estimators of C'β in the condition.
出处
《高校应用数学学报（A辑）》
CSCD
北大核心
1994年第4期429-434,共6页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
关键词
最小偏倚估计
G-M模型
线性变换
Minimum Bias Estimator
Best Linean Minimum Bias Estimator.
