正态均值线性估计的可容许性

Admissibility for the linear estimators of normal mean value

假定多元随机变量Y^Nn(β,σ2V),β∈Rn,σ2>0未知,V≥0已知;讨论了均值向量β的线性估计的可容许性,并在二次损失函数‖δ(Y)-β‖2下,得到了均值向量β的线性估计可容许的充要条件.

Suppose Y～Nn（β,σ^2V）,β∈R^n,σ^2〉0 are unknown parameters, while V≥0 is known, the admissibility of linear estimators of mean value vector β is discussed. Under quadratic loss function ‖δ（Y）-β‖^2, a necessary and sufficient condition for the admissibility of the linear estimators of normal mean vector β is given.