协方差改进法与半相依回归的参数估计  

Covariance Adjusted Approach and Parameter Estimation in Seemingly Unrelated Regression

作　　者：王松桂[1] 严利清[2] 

机构地区：[1]北京工业大学 [2]中国科技大学,合肥230026

出　　处：《应用概率统计》1997年第3期288-296,共9页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金;北京市自然科学基金资助项目

摘　　要：对于由两个误差项相关的线性回归方程组成的系统,本文应用协方差改进法获得了参数的一个迭代估计序列。我们证明了当协方差阵已知时,该估计序列处处收敛到最佳线性无偏估计,且它们的协方差阵在矩阵偏序意义下单调下降收敛到最佳线性无偏估计的协方差阵,该估计序列具有Pitman准则下的优良性。当协方差阵未知时,我们证明了用协方差阵的无限制估计所产生的两步估计具有无偏性、相合性和渐近正态性。在一定意义下,本文的估计优于文献中已有的一些估计。本文的结果也显示了协方差改进方法的有效性。For a seemingly unrelated regression with two linear regressionb models, a sequence of estimators is proposed by using the covariance adjusted approach. It is proved that the sequence converges everywhere to the best linear unbised estimator(BLUE) and their covariance matrices converge monotonically to that of the BLUE if the covariance matrix of the errors is known. The sequence has also some optimalities under Pitman criterion of closeness. When the covariance matrix of the errors is undnown, the unbiasedness, the consistency and the saymptotic normaluity of the two-stage estimators of the sequence are proved. The results obtained in this paper show also the power of the covariance adjusted approach.

关 键 词：协方差 改进法 线性回归 半相依回归 参数估计 

分 类 号：O212.1[理学—概率论与数理统计]