Letθbe a p×l parameter vector. Let T<sub>1</sub> and T<sub>2</sub> be two vector statistics of orders pand q such that E（T<sub>1</sub>） =θand E（T<sub>2</sub>）...Letθbe a p×l parameter vector. Let T<sub>1</sub> and T<sub>2</sub> be two vector statistics of orders pand q such that E（T<sub>1</sub>） =θand E（T<sub>2</sub>）=0 and their Joint covariance matrix is given bywhere σ<sup>2</sup> is unknown, Σ is known positive definite matrix, denoted henceforth by Σ】0. It iswell known that T<sub>1</sub> is not uniformly minimum variance unbiased estimator if Σ<sub>1</sub>2≠0. Raosuggested a better estimator θ<sup>*</sup> = T<sub>1</sub>—Σ<sub>1</sub>2Σ<sub>2</sub>2<sup>1</sup>T<sup>2</sup>, called covariance-improved estimator展开更多
For a seemingly unrelated regression system consisting of m equations, the information contained in all the equations is divided into sample information and additional information, and a new estimate of the regression...For a seemingly unrelated regression system consisting of m equations, the information contained in all the equations is divided into sample information and additional information, and a new estimate of the regression coefficients is proposed by using successive superposition. More precisely, the following three problems are solved: (ⅰ) a statistic summarized the additional information is constructed, (ⅱ) a procedure which superposes the additional information on the sample information and a new estimate of regression coefficients are proposed, (ⅲ) some properties of the new estimate are established.展开更多
基金Project supported partially by the National Natural Science Foundation of China and the Beijing Natural Science Foundation.
文摘Letθbe a p×l parameter vector. Let T<sub>1</sub> and T<sub>2</sub> be two vector statistics of orders pand q such that E（T<sub>1</sub>） =θand E（T<sub>2</sub>）=0 and their Joint covariance matrix is given bywhere σ<sup>2</sup> is unknown, Σ is known positive definite matrix, denoted henceforth by Σ】0. It iswell known that T<sub>1</sub> is not uniformly minimum variance unbiased estimator if Σ<sub>1</sub>2≠0. Raosuggested a better estimator θ<sup>*</sup> = T<sub>1</sub>—Σ<sub>1</sub>2Σ<sub>2</sub>2<sup>1</sup>T<sup>2</sup>, called covariance-improved estimator
基金Project partially supported by the National Natural Science Foundation of China and by the Third World Academy of Sciences under grant No. 87-46.
文摘For a seemingly unrelated regression system consisting of m equations, the information contained in all the equations is divided into sample information and additional information, and a new estimate of the regression coefficients is proposed by using successive superposition. More precisely, the following three problems are solved: (ⅰ) a statistic summarized the additional information is constructed, (ⅱ) a procedure which superposes the additional information on the sample information and a new estimate of regression coefficients are proposed, (ⅲ) some properties of the new estimate are established.
