【摘要】 对于线性模型ＥＹ＝ Ｘβ，ＣｏｖＹ＝ ∑ｍｉ＝ １σ２Ｖｉ。当Ｓβ不可估时，本文分别给出了Ｓβ的线性估计在二次损失和矩阵损失下线性可容许的充要条件。当Ｙ～Ｎ（Ｘβ，∑ｍｉ＝ １ σ２Ｖｉ） 时，还得到了Ｓβ的线性估计在矩阵损失下在一切估计类中可容许的充要条件和在二次损失下在一切估计类中可容许的充分条件和必要条件更多还原

【Abstract】 For the linear model EY=Xβ, Cov Y=∑ m i=1 σ 2V i, for the case that Sβ is not estimable, this paper has given the necessary and sufficient conditions for any linear estimator of Sβ to be linear admissible under quadratic and matrix loss, respactively. If Y～N(Xβ,∑ m i=1 σ 2V i), we have obtained the necessary and sufficient conditions for any linear estimator of Sβ to be admissible under matrix loss in the class of all estimators, and the necessary conditions and sufficient conditions for any linear estimator of Sβ to be admissible under quadratic loss in the class of all estimators.更多还原