线性模型中共同均值的线性估计的可容许性

ADMISSIBILITY OF LINEAR ESTIMATORS OF THE COMMON MEAN VECTOR IN LINEAR MODEL

文章对于共同均值模型的共同均值的线性(包含齐线性与非齐线性)估计的可容许性,给出了共同均值的线性组合Sβ的线性估计的可容许的充分必要条件。在文章的证明过程中用了矩阵微商的方法。

Consider the linear model: Y_i=(y_1^(i),…,y_n^(i))'=β+ε_i=(β_1,…, β_n)＇+(ε_1^(i)…,ε_n^(i))＇ i=1,…,m where Y_1,…, Y_m are independent, E (ε_i)=0, Var (ε_i)=σ_i^2V,i= 1,…, m. β∈R^n, 0<σ_i^2< ∞ unknown. The necessary and sufficient conditions that sum from i=1 to m A_iY_i and sum from i=1 to m A_iY_i+C are admissible for Sβ within the classes {sum from i=1 to m A_iY_i; A_i: s×n} and {sum from i=1 to m A_iY_i+C; A_i: s×n, C: s×1} are given respectively. In comparision with the method used in other papers, we use the method of matrix derivative.