Optimality and Recursive Algorithm of General Least Squares Estimator of Seemingly Unrelated Linear Regression Models

Based on the problem how to model Seemingly Unrelated linear models with different batches of samples, the paper raises the method of getting rid of the stale and taking in the fresh. The method of taking in the fresh is that first, with a group of samples gotten to establish the linear model and receive least squares estimation; Second , the second batch of samples of data is received, re-use the first batch of samples operations, the outcomes of the two batches of samples are integrated with the least-squares estimation of linear models, and thus obtain the recursive algorithm of least squares estimation; The method of getting rid of the stale, contrary to the method of bringing into the fresh, excludes the old sample information and thus obtains a recursive algorithm of least-squares estimation; the method of getting rid of the stale and taking in the fresh is the recursive algorithm integrated with the above two kinds of recursive algorithms. The paper proposes the recursive algorithm of generalized least squares estimator of Seemingly Unrelated linear regression models under the given conditions, and showed, under the Mean Dispersion Error(MDE) criterion, that increasing the sample size will increase the estimation accuracy .