相依回归系统一种协方差改进估计之协方差阵的无偏估计  

UNBIASED ESTIMATORS OF THE COVARIANCE MATRIS OF COVARIANCE IMPROVED ESTIMATORS IN TWO SEEMINGLY UNRELATED REGRESSIONS

作　　者：刘金山[1] 

机构地区：[1]五邑大学数理系

出　　处：《纯粹数学与应用数学》1997年第1期30-37,共8页Pure and Applied Mathematics

基　　金：河南省自然科学基金

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.

关 键 词：相依回归 两步估计 协方差阵估计 无偏估计 回归 

分 类 号：O212.1[理学—概率论与数理统计]