矩阵损失下多元Gauss-Markov模型中可估函数的线性Minimax估计

Linear Minimax estimators of estimable function in multiple Gauss-Markov model with matrix loss function

对一般多元Gauss-Markov模型E(Y)=XB,cov(Y)=σ2∑V,∑,V是正定矩阵,SB是线性可估函数.本文给出了线性Minimax估计的定义,在给定的两种矩阵损失函数下,分别获得了可估函数SB在线性估计类中唯一的线性Minimax估计.

For a general multiple Gauss-Markov model E（Y）=XB,cov（Y）=σ2∑V,∑ and V are the positive definitive matrices,and SB is an estimable function.The paper gave the definition of the linear Minimax estimator.Moreover,it obtained respectively the unique linear minimax estimator of the estimable function SB in linear estimator with two specified matrix loss functions.