平衡损失下一般Gauss-Markov模型中回归系数的最优估计（英文）

在平衡损失下,我们研究了一般Gauss-Markov模型中回归系数的最优估计,首先我们得到了线性估计为最佳线性无偏估计的充分必要条件;其次证明了平衡损失下的最佳线性无偏估计在几乎处处意义下是唯一的,并且是普通最小二乘估计和二次损失下最优估计的平衡;最后,我们讨论了最优估计关于损失函数和模型设定的稳健性,并得到了该最优估计在模型误定下具有稳健性的充分必要条件.

Optimal Estimator of Regression Coefficient in a General Gauss-Markov Model under a Balanced Loss Function

In this paper, we investigate optimal estimator of regression coefficient in a general Gauss-Markov model under balanced loss function. Firstly, necessary and sufficient conditions for linear estimators to be best linear unbiased estimator (BLUE) are provided. Secondly, we prove the best linear unbiased estimator is unique in the sense of almost everywhere, and also a balance between least squares estimator and optimal estimator under quadratic loss. Thirdly, loss robustness of the optimal estimator is discussed in terms of relative losses and relative saving losses. Finally, we give some conditions about the robust BLUE on the mis-specification of covariance matrix.