一类统计模型相应风险的极小极大估计

The Minimax Estimation of Corresponding Risk of Statistical Model

关于风险估计,Bunke曾讨论了一类多参数控制的线性模型在带正定"加权"矩阵的二次损失函数下,最佳线性无偏估计量的极小极大性.然而,对于相应风险中具有大估计误差的不合理加权,上述损失函数已不适用.为此,本文提出了一类更为理想的二次损失函数,并在此损失函数下,对相关风险进行了极小极大估计与比较.讨论结果表明,本文提出的二次损失函数是合理与适用的.

Concerning the risk estimation, Bunke discussed the minimax of the best linear unbiassed estimator of a multiparameter controled statistical model which has the quadratic loss function with the positive definite ＂weighting＂ matrix, But to the unjustifiable weighting that has large estimation errors on the corresponding risk shis quadratic loss function is not applicable. So the present article proposed a more ideal quadratic loss function,and made the minimax estimators and comparisons on the correlated risk. The discussion shows that the proposed quadratic loss function is rational and applicable.