正态线性模型中可估函数的极小极大估计(英文)

On Minimax Estimators of Estimable Functions in Normal Linear Experiments

论述正态线形模型NL(Xβ,δ~2V),其中V为已知k×n正定矩阵,σ~2>0为未知参数,在二次损失|σ~2+β~TX^TV^1Xβ|~1||δ SXβ||下,根据可容许性理论,证明了SXβ的线性估计是其一切估计类中的唯一极小极大估计。

This paper sheds light on the normal linear experiment NL( Xβ, σ2 V) where V is a known k × n positive definite matrix, cr is an unknown positive parameter. Under quadratic loss function [ σ2+βTXTV-1Xβ]-1‖δ-SXβ‖, by the theory of admissibility, this paper proves that a linear estimator for SXβ is the unique minimax estimator in the class of all estimators.