| 加权平方损失下一类指数分布族刻度参数的估计 |
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| 引用本文： | 徐宝,宋立新.加权平方损失下一类指数分布族刻度参数的估计[J].黑龙江大学自然科学学报,2009,26(6). |
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| 作者姓名： | 徐宝 宋立新 |
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| 作者单位： | 吉林师范大学,数学学院,四平,136000 |
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| 基金项目： | 吉林省教育厅科技基金资助项目，吉林省教育厅高等教育教学改革立项课题 |
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| 摘 要： | 对一类刻度指数分布族c(x,n)θ~(-y)e~-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.
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| 关 键 词： | 加权平方损失 最小风险同变估计 Bayes估计 最小最大估计 不变性 |
Estimator of the scale-parameter in a class of the exponential family under weighted quadratic loss function |
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| XU Bao,SONG Li-xin.Estimator of the scale-parameter in a class of the exponential family under weighted quadratic loss function[J].Journal of Natural Science of Heilongjiang University,2009,26(6). |
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| Authors: | XU Bao SONG Li-xin |
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| Abstract: | For exponential family c(x,n)θ~(-y)e~-T(x)/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 θ,and the minimaxity of minimum risk equivariant estimator is discussed.The invariance of Bayes estimator is proved by using the theory of intergral transformation. |
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| Keywords: | weighted quadratic loss Minimum risk equivariant estimator Bayes estimator Minimax estimator invariance |
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