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(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].
