I. INTRODUCTIONIt is well-known that the usual estimator, the sample mean, for the mean of a multivariate normal distribution is inadmissible. After the improvement of the original proof, several concise proofs are pr...I. INTRODUCTIONIt is well-known that the usual estimator, the sample mean, for the mean of a multivariate normal distribution is inadmissible. After the improvement of the original proof, several concise proofs are proposed, referring to Anderson, for example.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
We consider estimation of the scale parameter of a two-parameter exponential distribution on the basis of doubly censored data.Classes of estimators,improving upon the minimum risk equivariant estimator,are derived un...We consider estimation of the scale parameter of a two-parameter exponential distribution on the basis of doubly censored data.Classes of estimators,improving upon the minimum risk equivariant estimator,are derived under an arbitrary strictly convex loss function.Some existing dominating procedures are shown to belong to the proposed classes of estimators.展开更多
Let X_1,...,Xn. be a random sample from multivariate normal distribution Np(μ,∑), where μ∈Rp and E is a positive definite matrix, both p and ∑ being unknown. It is shown that for the entropy loss L(δ, |∑| ^(- 1...Let X_1,...,Xn. be a random sample from multivariate normal distribution Np(μ,∑), where μ∈Rp and E is a positive definite matrix, both p and ∑ being unknown. It is shown that for the entropy loss L(δ, |∑| ^(- 1) )=δ/ |∑| ^(- 1) -log(δ/ |∑ |~ (- 1) ) - 1 , the best affine equivariant estimator of the generalized precision |∑|^(-1) is inadmissible and three classes of improved estimators are given.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘I. INTRODUCTIONIt is well-known that the usual estimator, the sample mean, for the mean of a multivariate normal distribution is inadmissible. After the improvement of the original proof, several concise proofs are proposed, referring to Anderson, for example.
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We consider estimation of the scale parameter of a two-parameter exponential distribution on the basis of doubly censored data.Classes of estimators,improving upon the minimum risk equivariant estimator,are derived under an arbitrary strictly convex loss function.Some existing dominating procedures are shown to belong to the proposed classes of estimators.
基金the National Natural Science Foundation of ChinaNow at Department of Mathematics, Huaiyin Teachers' College, Jiangsu, China
文摘Let X_1,...,Xn. be a random sample from multivariate normal distribution Np(μ,∑), where μ∈Rp and E is a positive definite matrix, both p and ∑ being unknown. It is shown that for the entropy loss L(δ, |∑| ^(- 1) )=δ/ |∑| ^(- 1) -log(δ/ |∑ |~ (- 1) ) - 1 , the best affine equivariant estimator of the generalized precision |∑|^(-1) is inadmissible and three classes of improved estimators are given.
