一般方差分量模型中回归系数的线性估计的可容许性

Admissibility of Linear Estimators of Regression Coefficient in a General Variance Component Model

考虑方差分量模型EY=Xβ,COV(Y)=∑i=1θiVi,其中n×p矩阵X和非负定矩阵Vi(i=1,2,…,m)都是已知的,β∈Rp,θiE0或θi>0(i=1,2,…,m)均为参数.在本文中,我们在二次损失下,当V=∑mi=1ViE0时,给出了关于可估函数Sβ的线性估计在线性估计类中可容许性的充要条件,从而有效地把文[5]的主要结果推广为最一般情形.

Consider the general variance component model EY=Xβ, COV(Y)=∑mi=1θ_iV_i,where X: nxp and V_i0(i=1,2,...,m) are known, β∈Rp,θ_i0 and θ_i>0 (i=1,2,=,m) are parameters. When V=∑mi=1V_i0,the sufficient and necessary conditions for a linear estimable estimator of Sβ to be admissible in the class of all linear estimators are given under quadratic loss function.