In this note, as an example, we introduoe a definition of general optimality in estimating a linear estimable function S<sub>k×p</sub> （S’ μ（X’）） of the mean matrix in multivariate linear mod...In this note, as an example, we introduoe a definition of general optimality in estimating a linear estimable function S<sub>k×p</sub> （S’ μ（X’）） of the mean matrix in multivariate linear model: Y<sub>n×m</sub>=X<sub>n×p</sub> +ε E（ε）=0, Cov（ ）=σ<sup>2</sup>U<sub>n×n</sub> V<sub>m×m</sub>, n≥m. In general, the general optimality of a parametric matrix follows analogously. The above X, S, U≥0 and V≥0 （but V≠0） are known matrix, and σ<sup>2</sup>】0 are unknown parameters, =（ε<sub>1</sub>’, ε<sub>2</sub>’, …, ε<sub>n</sub>’）’, where ε<sub>i</sub> is the ith row of ε, U V denotes the展开更多
A generalization of Zellner’s balanced loss function is proposed. General admissibility in a general multivariate linear model is investigated under the generalized balanced loss function. And the sufficient and nece...A generalization of Zellner’s balanced loss function is proposed. General admissibility in a general multivariate linear model is investigated under the generalized balanced loss function. And the sufficient and necessary conditions for linear estimators to be generally admissible in classes of homogeneous and nonhomogeneous linear estimators are given, respectively.展开更多
文摘In this note, as an example, we introduoe a definition of general optimality in estimating a linear estimable function S<sub>k×p</sub> （S’ μ（X’）） of the mean matrix in multivariate linear model: Y<sub>n×m</sub>=X<sub>n×p</sub> +ε E（ε）=0, Cov（ ）=σ<sup>2</sup>U<sub>n×n</sub> V<sub>m×m</sub>, n≥m. In general, the general optimality of a parametric matrix follows analogously. The above X, S, U≥0 and V≥0 （but V≠0） are known matrix, and σ<sup>2</sup>】0 are unknown parameters, =（ε<sub>1</sub>’, ε<sub>2</sub>’, …, ε<sub>n</sub>’）’, where ε<sub>i</sub> is the ith row of ε, U V denotes the
基金supported by the Excellent Youth Talents Foundation of University of Anhui (Grant Nos.2011SQRL127 and 2012SQRL028ZD)
文摘A generalization of Zellner’s balanced loss function is proposed. General admissibility in a general multivariate linear model is investigated under the generalized balanced loss function. And the sufficient and necessary conditions for linear estimators to be generally admissible in classes of homogeneous and nonhomogeneous linear estimators are given, respectively.
