正态线性试验中可估函数的最小最大估计

On Minimax Estimators of Estimable Funetions in Normal Linear Experiments

对于正态线性试验NL(Xβ,δ~2V),V为已知κ×n阶正定矩阵,δ~2为未知正参数,通过容许性理论,在平方损失函数(δ~2+β~rX^rV^(-1)Xβ)^(-1)‖δ-SXβ‖下,本文证明了SXβ的线性估计是所有估计类中一致最小最大估计。

For the normal linear experiment NL( Xβ, σ2 V) where V is a known k × n positive definite matrix, σ2 is a unknown positive paremeter, under qudratic loss function [σ2 +βrXrV-1Xβ-1||δ - SXβ|| , by the theory of admissibility, this paper proves that a linear estimator for SXβ is the unique minimax estimator inb the class of all eatimators.