加权p,q对称熵损失下一类指数分布模型参数的估计  

Estimator of the Parameter in a Subclass of the Exponential Model under Weighted p,q Symmetric Entropy Loss

作　　者：徐宝[1] 姜玉秋[1] 滕飞[1] 宋立新[1] 

机构地区：[1]吉林师范大学数学学院,吉林四平136000

出　　处：《数学的实践与认识》2012年第7期186-190,共5页Mathematics in Practice and Theory

基　　金：吉林省教教育厅"十一五"科学技术研究项目(2010350);四平市科技发展计划资助项目(2010010)

摘　　要：在由信息论中的熵演绎出的一种新损失一加权P,q对称熵损失L(θ,δ)=θ/Pδp+δq/qθq-2(ρ,q>0)下,研究了一类指数分布模型c(x,η)θ-νe-νe-T(x)/θ的参数θ的Bayes估计的一般形式与精确形式,讨论了参数θ的形如cT(X)+d的一类估计的可容许性与不可容许性,并应用积分变换定理证明了参数θ的Bayes估计与可容许估计具有不变性,For exponential model c（x,n）θ-ve-T（x）θ, we dealt with the Bayes estimator and admissible estimator of scale parameter θ under a new loss-weighted p, q symmetric entropy loss L（θ,δ）=θp/pδp＋δq/qθq-20,q〉0）which deduced from entropy that related to theory of information. The general and exact form of the Bayes estimator were obtained. The admissibility and inadmissibility of a class of linear estimators of the form cT（X） ＋ d were studied. The invariance of the two estimators was proved using the theorem integral transform.

关 键 词：加权P q对称熵损失 BAYES估计 可容许估计 不变性 

分 类 号：O211.3[理学—概率论与数理统计]