摘要:
对于m(≥3)SUR模型(1),其设计矩阵满足条件(4),本文得到了回归系数βi(i=1,…,m)的两步Aitken估计的精确协方差表达式,从而获得了两步估计优于LS估计的有限样本性质。特别是,当m=3时本文结果可以与Revankar(1974)给出的一类两方程SUR模型结果相比较.
Abstract:
For m(≥3) seemingly unrleated regression equations: yi = Xiβi+εi,(i=1,…, m), with P1 =… = Pk, Pk+1 =… = Ps, Ps+1 =… = Pm and P1 =Ps+Pm, where Pi = Xi(X'iXi)-1X'i,the exact finite sample covariance matrix of Zellner’s two-step Aitken estimator ~βi of βi(i =1…,m), based on the unrestricted estimate S of ∑ = (σij ) are obtained.When m = 3, all the three ~βi (i = 1, 2, 3) are shown to be more efficient then the OLS estimators of βi, for moderate departures of $\rho_{i j}^2=\sigma_{i j}^2 / \sigma_{i i} \sigma_{j j}$$ from zero, and the efficiencies are shown to be increased with the sample size n. These results can be compared with those obtained by Revankar(1974)for a system of 2SUR with X1=(X2,L)