刻度参数同变估计类L_1中估计的ε稳定性

ε-Stability of Estimation for a Class of Equivariant Estimators L_1 of the Scale Parameter

采用统计判决中的最优准则方法,讨论了在平方损失函数下与刻度参数的最小风险同变估计Tn有关的一般同变估计类L1=Tn1+∑n-1i=1ciXiXn中估计的ε稳定性问题,给出了此估计类中估计的ε稳定性条件,并用该方法讨论了Γ分布族刻度参数λ估计的ε稳定性.

The present paper is proposed a method to deal with the ε-stability of estimation for a class of equivariant estimators L_1=T_n1+∑n-1i=1c_iX_iX_n under the loss function L(σ,d)=1-dσ 2 by means of the optimal criterion in the statistical decision. The conditions of the ε-stability for the estimator in L_1 are presented. Furthermore, as an example of this method, the ε-stability of estimation of scale paramter λ in Gamma distribution is discussed.