IMPROVED ESTIMATION OF THE GENERALIZED PRECISION UNDER THE ENTROPY LOSS  

作　　者：孙孝前 彭运佳 

出　　处：《Acta Mathematicae Applicatae Sinica》2000年第2期162-170,共9页应用数学学报（英文版）

基　　金：the National Natural Science Foundation of China;Now at Department of Mathematics, Huaiyin Teachers' College, Jiangsu, China

摘　　要：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.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.

关 键 词：Best affine equivariant estimator generalized precision INADMISSIBILITY entropy loss 

分 类 号：O186[理学—数学]