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...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.展开更多
In the system of m （m ≥ 2） seemingly unrelated regressions, we show that the Gauss-Markov estimator （GME） of any regression coefficients has unique simplified form, which exactly equals to the one- step covarianc...In the system of m （m ≥ 2） seemingly unrelated regressions, we show that the Gauss-Markov estimator （GME） of any regression coefficients has unique simplified form, which exactly equals to the one- step covariance-adjusted estimator of the regression coefficients, and hence we conclude that for any finite k ≥ 2 the k-step covariance-adjusted estimator degenerates to the one-step covariance-adjusted estimator and the corresponding two-stage Aitken estimator has exactly one simplified form. Also, the unique simplified expression of the GME is just the estimator presented in the Theorem 1 of Wang＇ work [1988]. A new estimate of regression coefficients in seemingly unrelated regression system, Science in China, Series A 10, 1033-1040].展开更多
基金supported by the National Natural Science Foundation of China(Grant No.10271001).
文摘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.
基金Supported by the National Natural Science Foundation of China(No.11371051)
文摘In the system of m （m ≥ 2） seemingly unrelated regressions, we show that the Gauss-Markov estimator （GME） of any regression coefficients has unique simplified form, which exactly equals to the one- step covariance-adjusted estimator of the regression coefficients, and hence we conclude that for any finite k ≥ 2 the k-step covariance-adjusted estimator degenerates to the one-step covariance-adjusted estimator and the corresponding two-stage Aitken estimator has exactly one simplified form. Also, the unique simplified expression of the GME is just the estimator presented in the Theorem 1 of Wang＇ work [1988]. A new estimate of regression coefficients in seemingly unrelated regression system, Science in China, Series A 10, 1033-1040].
