一类理想二次损失函数下多参数统计模型的风险估计

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 ,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 .结果表明 ,所提出的二次损失函数是合理的、适用的

Risk estimation of multi-parameter statistical model of an ideal quadratic loss function

The minimax of the best linear unbiased estimator of a multi-parameter control statistical model, which has the positive definite "weighting" matrix of quadratic loss function, is discussed. But to the unjustifiable weighting that has great estimation errors on the corresponding risk, this quadratic loss function is not applicable. So in this paper, a more ideal quadratic loss function is put forward, from which the minimax estimators and comparisons of relative risk are made. The discussion shows that the quadratic loss function in this paper is rational and applicable.