作 者: ;
机构地区: 五邑大学数学物理系
出 处: 《纯粹数学与应用数学》 1997年第1期30-37,共8页
摘 要: 考虑相依回归方程系统yi=Xiβi+εi(i=1,2),E(εi)=0,Cov(εi,εj)=σijIn.记βi为βi的协方差改进估计[1].σij未知时,记βi为用非限定估计σij代替βi中的σij得到的两步估计,并记βi为用限定估计σij代替βi中的σij得到的两步估计,这两种两步估计的协方差中含有未知参数σij.本文对于一般系统给出βi的协方差阵V(βi)的无偏估计,并对于文献中经常考虑的一类系统给出βi的协方差阵V(βi)的无偏估计.这些估计可用于求标准差和置信区间的实际计算.通过比较可知。 This paper considers the system of two seemingly unrelated regressions : y i=X iβ i+ε i ( i=1, 2), E(ε i)=0, Cov (ε i, ε j)=σ ij I n. Let i be the Covariance Improved Estimator of β i and i be the two-step estimator of i based on the unrestricted estimate of Σ, and i be the two-step estimator of i based on the rstricted estimate of Σ . The unbiased estimator of the cobariance matrix V( i) is also derived for a class of system considered in some papers. These derivations facilitate the construction of the finite-sample standard errors for the two-step estimators of the individual regression coefficients. Comparisons are made between the unbiased estimator and the conventional consistent estimator under mean square error matix criterion.