对称损失下一类刻度分布族参数的估计

Estimator of Parameter in a Scale Family under a Symmetric Loss

在q对称熵损失函数L(θ,δ)=qθ/qδ+qδ/qθ-2(0<q<ν)下研究刻度分布族c(x,n)θ-νe-T(x)/θ参数θ的估计,得到了θ的最小风险同变(MRE)估计及Bayes估计的一般与精确形式,并讨论了θ的形如cT(X)+d的一类线性估计的可容许性和不可容许性以及θ的MRE估计的最小最大性.

For scale family c（x,n）θ^-v e^-T（x）/θ, we dealt with the estimator of parameter θ under q-symmetric entropy loss L （θ,δ）=θ^q/δ^q＋δq^/θ^q-2（0〈q〈v）.The general and exact form of the MRE estimator and Bayes estimator were obtained. The admissibility and inadmissibility of a class of linear estimators of the form cT（X） ＋ d and the minimaxity of the MRE estimator were studied.