一类相依回归系统参数的有偏估计

THE BIASED ESTIMATORS OF THE PARAMETERS IN THE TWO SEEMINGLY UNRELATED REGRESSION SYSTEM

对于一类相依线性回归系统(1.1),许多作者研究了回归参数的最小二乘估计的改进,这些改进估计都是无偏估计且在通常情况下具有许多优良性质,但是在设计阵呈病态时这些改进估计的均方误差都很大,因而在这种情况下不再被认为是良好估计。针对这种情况,本文提出了两种有偏估计,证明了在设计阵呈病态时这些有偏估计的优良性质并研究了与之有关的检验问题。

For the two seemingly unrelated regression system (1.1), some authors have investigated the improvement of the least squares estimators of the regression parameters. These improved estimators are all unbiased and have many advantages. But their mean square errors are large when the design matrix is ill-conditioned. In this paper, we proposed two kinds of biased estimators which have some superiority to the unbiased estimators.