一般线性模型中参数的平衡广义LS估计

Balanced generalized LS estimation of the regressive coefficient

基于平衡损失的思想,对一般线性模型提出了一种全面地度量估计优良性的标准,给出了在此标准下回归系数的平衡广义最小二乘估计,并讨论了其优良性.得到了该估计为无偏估计的充分必要条件,以及在一定条件下,在均方误差损失的准则下平衡广义最小二乘估计优于最佳线性无偏估计的充分必要条件.

Based on the idea of balanced loss function, a new measuring standard for the estimations of uperiorities was proposed for general linear models. Under the new standard, the balanced generalized LS estimation of the regressive coefficient was derived. The necessary and sufficient condition for its unbiasedness was discussed and its superiority over BLUE in terms of the mean square error matrix criterion was studied.