多维指数族分布的参数线性容许估计的一个充分条件

Sufficient Condition for a Class of Linear Admissible Estimators in the Multi Parameter Exponential Family

本文利用唯一的Ｂａｙｅｓ估计是容许估计的原理，构造了一个先验分布π１（θ）＝Ｍβ－１（θ）ψ（θ）ｅｘｐ∑ｎｉ＝１∫θｉθｉ０ｂ－ｒｉ（ｔ）ａｉｎｄｔｉ，当它满足一定的条件时，证明了在均方损失下，多维指数族分布ｆθ（ｘ）＝β（θ）ｅｘｐθ′ｘ的参数ｒ（θ）的唯一Ｂａｙｅｓ估计为线性函数ａ′ｘ＋ｂ。

In this paper, we use the elements that the exclusive Bayes estimation is admissbility estimation, and construct the prior distcibution as π 1(θ)=Mβ -1 (θ)ψ(θ) exp ∑ni=1∫ θ i θ i 0 b-r i(t i)a in d t i, If it suffices certain conditions, we prove the admissbility of linear estimation of the form a′x+b, in the multe parameter exponential family in estimating r(θ) with quadratic loss.