一般半相依回归系统的协方差改进估计

摘要

For the system of Seemingly Unrelated Rcgression Equations given by rn(in this two linear regression models, y1 is a matrix of m × 1, y2 is a matrix of n × 1, m ≠ n), we obtained an iteration sequence of estimator by using the covariance-improved approach. It is proved that the sequence converges everywhere to the best linear unbiased estimator (BLUE) and their covariance matrixes converge monotonically to that of the BLUE if the covariance matrixof the errors is known.rn　　When the covariance matrix of the errors is unknown, we consider the optimality of the two-stage covariance-inproved estimator. Under normal distribution assumption on the random error, the unbiasedness, the asymptotic normality and the strong consistency of the two-stage estimator are proved. Furthmore, a weak consistency condition is obtained when the iteration step is infinite.rn　　In this paper we extended and inproved the covariance-improved estimator introduced by Wang Songgui, the results show clearly the power of the covariance-improved approach.%本文讨论了由两个不等阶的回归方程组成的半相依系统。运用协方差改进法获得了参数的一个迭代估计序列，并证明它在协方差阵已知时，处处收敛到最佳线性无偏估计，同时其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。当协方差阵未知时，证明了两步估计序列具有无偏性和渐进正态性，并且给出了当迭代次数亦趋于无穷时，保证其具有相合性的一个条件。本文结果拓广和改进了王松桂等的结果，进一步显示了协方差改进法的有效性。