尺度参数的最优尺度不变估计的非容许性

Inadmissibility of the Best Scale-invariant Estimator of Scale Parameters

本文针对尺度参数分布的情形，在一般二次损失函数下，证明了维数≥２时，最优尺度不变估计是非容许的，并得到了它的同时改进估计，据此讨论了此改进估计关于损失函数类的稳健性问题。在加权平方损失函数下，得到了不等尺度改进估计．对于多个观测值的情形，获得了两个非常有用的结果。

The present paper considers inadmissibility of the best scale-invariant estimatorδ_0(X)of scale parameters under general quadratic losses L_Q(θ,δ)=(θ-δ)′Q(θ-δ) whereQ is a positive definite matrix satisfying some conditions, obtaining simultaneously improvedestimator δ_0(X)+where C=(c,…,c)′and c is a suitable positive number. Wediscussed robust result of improved estimators againtqt loss functions. Under the weightedsquared-error losses, we developed unequal-shift improved estimators domination δ_0(X). Dealing with the case of multiple observations, we obtained new results that have not beenconsidered before.