矩阵损失下贝叶斯线性无偏估计及其稳健性

Bayesian linear unbiased estimator and its robustness under the matrix loss function

证明了,在一般线性模型中,未知参数在二次损失下的贝叶斯线性无偏估计也是矩阵损失下的贝叶斯线性无偏估计.讨论了贝叶斯线性无偏估计关于误差分布的稳健性,给出了未知参数的贝叶斯线性无偏估计是最优估计的充分必要条件.

It was proved that the Bayesian linear unbiased estimator of the unknown parameters in a general linear model under the quadratic loss function is also the Bayesian linear unbiased estimator under the matrix loss function. The robustness of the Bayesian linear unbiased estimator of the unknown parameter in terms of error distributions was also discussed; moreover, the necessary and sufficient conditions are obtained, under which the Bayesian linear unbiased estimator of the unknown parameters hold its optimality.