加权平方损失下一类指数分布族刻度参数的估计

Estimator of the scale-parameter in a class of the exponential family under weighted quadratic loss function

对一类刻度指数分布族c(x,n)θ-νe-T(x)/θ,利用加权平方损失函数L(θ,δ)=(δ/θ-1)2研究了刻度参数θ的最小风险同变估计。经由Bayes估计给出了最小风险同变估计的精确形式,并讨论了它的最小最大性,最后应用积分变换定理证明了θ的Bayes估计具有不变性。

For exponential family c（x,n）θ^-pe^-T（τ）θ, the minimum risk equivariant estimator is considered by using weighted quadratic loss L（θ,δ）=（δ/θ-1）2. The exact form of minimum risk equivariant estimator for θ is given via the generalized Bayes estimator of O, and the minimaxity of minimum risk equivariant estimator is discussed. The invariance of Bayes estimator is proved by using the theory of intergral transformation.