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
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
