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.
基金
the National Natural Science Foundation of China
Now at Department of Mathematics, Huaiyin Teachers' College, Jiangsu, China
