一类刻度参数指数分布族参数的最小风险同变估计

Minium risk equivariant estiamtor of the scale-parameter in a subclass of the exponential family

对Parsian(1996)与Jozani(2002)所研究的一类刻度参数指数分布族c(x,n)θ-νe-T(x)/θ,利用文献[1]提出的p,q对称熵损失函数L(θ,δ)=θp/δp+δq/θq-2(p,q>0),用参数估计方法,研究了刻度参数θ的最小风险同变估计与Bayes估计,并得到了它们的一般形式与精确形式,最后应用积分变换定理证明了Parsian(1996)未曾讨论的问题,即θ的最小风险同变估计具有最小最大性.

The scale-parameter family c（x, n） θ^-v e^-T（x）/θ was investigated by Parsian （1996） and Jozani （2002）. Using the method of parameter estimation, we dealt with the estimation of parameter θ under p,q-symmetric entropy loss L（θ,d）=θ^p/δ^p＋δ^q/θ^q-2（p,q〉0）. The general and exact form of the minimum risk equivariant estimation and Bayes estimation were obtained. Finally, using the theorem of intergral transform, we proved the existence of minimum or maximum of the minimum risk equivariant estimation which Parsian did not discuss.