半相依回归模型参数的协方差改进估计

本文研究了两个半相依回归系统的未知回归系数的估计问题。本文首先给出一种基于方差分量限定估计的两步协方差改进估计,并且给出了均方误差意义下优于最小二乘估计的条件。对于基于方差分量非限定估计的两步协方差改进估计,利用服从Wishart分布随机变量的可加性,本文给出了一种全新的估计形式,并且证明了该估计较文献中给出的两步协方差改进估计更加有效。

Improvement on the Covariance Estimation of Parameters in Seemingly Unrelated Regressions

The estimation of regression coeffcients in seemingly unrelated regressions with two linear regression models is considered in this paper. First, a covariance adjusted two-stage estimators based on the unrestricted estimate of variance component is obtained. A suffcient condition under which it dominates the least square estimation is derived. A new insight into covariance adjusted two-stage estimators based on the restricted estimate of variance component is discussed. Using the additive property of Wishart distribution variables, a new estimation is also obtained. Our new estimations provide more powerful availability.