Bayes and empirical Bayes iteration estimators in two seemingly unrelated regression equations  

作　　者：WANG Lichun 

机构地区：[1]Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing 100080, China

出　　处：《Science China Mathematics》2005年第9期1153-1168,共16页中国科学：数学（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.10271001).

摘　　要：For a system of two seemingly unrelated regression equations given by (?)(y_1 is an m×1 vector and y_2 is an n×1 vector,m≠n),employ- ing the covariance adjusted technique,we propose the parametric Bayes and empirical Bayes iteration estimator sequences for regression coefficients.We prove that both the covariance matrices converge monotonically and the Bayes iteration estimator squence is consistent as well.Based on the mean square error (MSE) criterion,we elaborate the su- periority of empirical Bayes iteration estimator over the Bayes estimator of single equation when the covariance matrix of errors is unknown.The results obtained in this paper further show the power of the covariance adiusted approach.For a system of two seemingly unrelated regression equations given by {y1=X1β+ε1,y2=X2γ+ε2, (y1 is an m × 1 vector and y2 is an n × 1 vector, m≠ n), employing the covariance adjusted technique, we propose the parametric Bayes and empirical Bayes iteration estimator sequences for regression coefficients. We prove that both the covariance matrices converge monotonically and the Bayes iteration estimator squence is consistent as well. Based on the mean square error (MSE) criterion, we elaborate the superiority of empirical Bayes iteration estimator over the Bayes estimator of single equation when the covariance matrix of errors is unknown. The results obtained in this paper further show the power of the covariance adjusted approach.

关 键 词：seemingly UNRELATED regressions  COVARIANCE adjusted approach  empirical BAYES estimation  mean square error criterion. 

分 类 号：N[自然科学总论]