一种对称损失函数下刻度参数的最优同变估计

本文研究刻度参数分布族(1/σ)f(x/σ)中刻度参数在损失函数L(σ,δ)=(σ-δ)~2/σδ下的最小风险同变估计及其最小最大性。

ESTIMATION OF SCALE PARAMETER UNDER A SYMMETRIC LOSS FUNCTION

In this paper, we propose a symmetric loss function for scale parameter of form $ L(\s,d)=\frac{d}{\s}+\frac{\s}{d}-2. $ This loss function can be viewed as a generalization of entropy loss and squared loss for scale $\s$. For scale family $\{\frac{1}{\s}f\Big(\frac {x}{\s}\Big),\s>0\}$, we find the minimum risk equivariant estimator(MRE) of $\s$, whose form is similar to that of Pitman's estimator under squared loss, and it is also proved that the MRE is a minimax estimator.