In this paper, we study the existence of the uniformly minimum risk equivariant (UMRE) estimators of parameters in a class of normal linear models, which include the normal variance components model, the growth curve ...In this paper, we study the existence of the uniformly minimum risk equivariant (UMRE) estimators of parameters in a class of normal linear models, which include the normal variance components model, the growth curve model, the extended growth curve model, and the seemingly unrelated regression equations model, and so on. The necessary and sufficient conditions are given for the existence of UMRE estimators of the estimable linear functions of regression coefficients, the covariance matrixV and (trV)α, where α > 0 is known, in the models under an affine group of transformations for quadratic losses and matrix losses, respectively. Under the (extended) growth curve model and the seemingly unrelated regression equations model, the conclusions given in literature for estimating regression coefficients can be derived by applying the general results in this paper, and the sufficient conditions for non-existence of UMRE estimators ofV and tr(V) are expanded to be necessary and sufficient conditions. In addition, the necessary and sufficient conditions that there exist UMRE estimators of parameters in the variance components model are obtained for the first time.展开更多
In this paper we investigate the estimator for the rth power of the scale parameter in a class of exponential family under symmetric entropy loss L（θ, δ） = v（θ/δ ＋ δ/θ - 2）. An exact form of the minimum ris...In this paper we investigate the estimator for the rth power of the scale parameter in a class of exponential family under symmetric entropy loss L（θ, δ） = v（θ/δ ＋ δ/θ - 2）. An exact form of the minimum risk equivariant estimator under symmetric entropy loss is given, and the minimaxity of the minimum risk equivariant estimator is proved. The results with regard to admissibility and inadmissibility of a class of linear estimators of the form cT（X） ＋ d are given, where T（X） Gamma（v, θ）.展开更多
In this paper,the definitions of Bayes estimator,minimax estimator,minimumrisk equivariant estimator and admissible estimator under the general matrix loss functionare given.Several results on estimation of parameters...In this paper,the definitions of Bayes estimator,minimax estimator,minimumrisk equivariant estimator and admissible estimator under the general matrix loss functionare given.Several results on estimation of parameters with the ordinary loss function areextended to the case of the matrix loss function.展开更多
Throughout this note, the following notations are used. For matrices A and B,A】B means that A-B is positive definite symmetric, A×B denotes the Kroneckerproduct of A and B R（A）, A’ and A<sup>-</sup&g...Throughout this note, the following notations are used. For matrices A and B,A】B means that A-B is positive definite symmetric, A×B denotes the Kroneckerproduct of A and B R（A）, A’ and A<sup>-</sup> stand for the column space, the transpose andany g-inverse of A, respectively; P<sub>A</sub>=A（A’A）<sup>-</sup>A’;for s×t matrix B=（b<sub>1</sub>…b<sub>t</sub>）,vec（B） de-notes the st-dimensional vector （b<sub>1</sub>′b<sub>2</sub>′…b<sub>t</sub>′）′, trA stands for the trace of the square ma-trix A.展开更多
基金This work was supported by the National Natural Science Foundation of China (Grant No. 19871088).
文摘In this paper, we study the existence of the uniformly minimum risk equivariant (UMRE) estimators of parameters in a class of normal linear models, which include the normal variance components model, the growth curve model, the extended growth curve model, and the seemingly unrelated regression equations model, and so on. The necessary and sufficient conditions are given for the existence of UMRE estimators of the estimable linear functions of regression coefficients, the covariance matrixV and (trV)α, where α > 0 is known, in the models under an affine group of transformations for quadratic losses and matrix losses, respectively. Under the (extended) growth curve model and the seemingly unrelated regression equations model, the conclusions given in literature for estimating regression coefficients can be derived by applying the general results in this paper, and the sufficient conditions for non-existence of UMRE estimators ofV and tr(V) are expanded to be necessary and sufficient conditions. In addition, the necessary and sufficient conditions that there exist UMRE estimators of parameters in the variance components model are obtained for the first time.
基金The SRFDPHE(20070183023)the NSF(10571073,J0630104)of China
文摘In this paper we investigate the estimator for the rth power of the scale parameter in a class of exponential family under symmetric entropy loss L（θ, δ） = v（θ/δ ＋ δ/θ - 2）. An exact form of the minimum risk equivariant estimator under symmetric entropy loss is given, and the minimaxity of the minimum risk equivariant estimator is proved. The results with regard to admissibility and inadmissibility of a class of linear estimators of the form cT（X） ＋ d are given, where T（X） Gamma（v, θ）.
文摘In this paper,the definitions of Bayes estimator,minimax estimator,minimumrisk equivariant estimator and admissible estimator under the general matrix loss functionare given.Several results on estimation of parameters with the ordinary loss function areextended to the case of the matrix loss function.
文摘Throughout this note, the following notations are used. For matrices A and B,A】B means that A-B is positive definite symmetric, A×B denotes the Kroneckerproduct of A and B R（A）, A’ and A<sup>-</sup> stand for the column space, the transpose andany g-inverse of A, respectively; P<sub>A</sub>=A（A’A）<sup>-</sup>A’;for s×t matrix B=（b<sub>1</sub>…b<sub>t</sub>）,vec（B） de-notes the st-dimensional vector （b<sub>1</sub>′b<sub>2</sub>′…b<sub>t</sub>′）′, trA stands for the trace of the square ma-trix A.
