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加权p,q对称熵损失下一类指数分布模型参数的估计
引用本文:徐宝,姜玉秋,滕飞,宋立新.加权p,q对称熵损失下一类指数分布模型参数的估计[J].数学的实践与认识,2012,42(7):186-190.
作者姓名:徐宝  姜玉秋  滕飞  宋立新
作者单位:吉林师范大学数学学院,吉林四平,136000
基金项目:吉林省教教育厅“十一五”科学技术研究项目,四平市科技发展计划资助项目
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,

关 键 词:加权p  q对称熵损失  Bayes估计  可容许估计  不变性

Estimator of the Parameter in a Subclass of the Exponential Model under Weighted p, q Symmetric Entropy Loss
XU Bao , JIANG Yu-qiu , TENG Fei , SONG Li-xin.Estimator of the Parameter in a Subclass of the Exponential Model under Weighted p, q Symmetric Entropy Loss[J].Mathematics in Practice and Theory,2012,42(7):186-190.
Authors:XU Bao  JIANG Yu-qiu  TENG Fei  SONG Li-xin
Institution:(Faculty of Mathematics,Jilin Normal University,Siping 136000,China)
Abstract:For exponential model c(x,n)θ(-v)e-T(x)/θ,we dealt with the Bayes estimator and admissible estimator of scale parameterθunder a new loss-weighted p,q symmetric entropy loss L(θ,d) =θp/pδpq/qθq -2(p,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.
Keywords:weighted p  q symmetric entropy loss  Bayes estimator  admissible estimator  invariance
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