SUR回归系统部分方程系数Zellner估计的有限样本性质

Some Exact Finite Sample Properties of Zellner’s Seemingly Unrelated Regression Equations Estimates

摘要: 对于SUR回归系统（1）,本文在弱于2,3和4的条件X'₁X_i（i=2,…,m）下考虑第一个方程系数β₁的Zellner的两步估计（4）,得到了β₁基于非限定残差的两步估计\hat\beta_Z 1的均方误差矩阵精确结果,由此结果容易得到3,4和5给出的已知结果。

Abstract: This paper considers Zellner’s "Aitken" estimator \hat\beta_Z 1 of β₁ based on the unrestricted estimate S of Σ =（σ_ij） in the system of m seemingly unrelated regressions: Y_i = X_iβ_i +ε_i（i = 1, …, m）,and derive finite sample variance matrix of the \hat\beta_Z 1 under the condition X'₁X_i（i=2,…,m）. This condition is weaker than the condition X'_iX_j = 0（i≠j,i,j = 1, …,m） considered by Zellner （1963）,Kataota （1967） and Revanker （1974）.