【作者】 李洪静；

【导师】 宋立新；

【作者基本信息】 大连理工大学 ， 应用数学， 2007， 硕士

【摘要】 在统计决策理论中，对称损失函数是一类重要的损失函数．比如平方损失函数，刻画了如果参数估计量与真值很接近，则该估计量对应较小的损失，是合理的；如果偏离得远，则该估计量对应较大的损失量，是不合理的．事实上，参数估计的优劣很大程度上依赖于损失函数形式的选择，因此有必要对不同的损失函数下参数估计的性质进行研究．本篇论文给出了α-对称熵损失下逆高斯分布在均值参数已知时形状参数的Bayes估计，并讨论了形如（cT+d）^-1的一类估计的容许性问题．本文在第一部分简要介绍了逆高斯分布；第二部分简单回顾了与Bayes决策有关的理论发展背景、决策基本原理、决策准则以及决策函数的容许性等问题；第三部分主要讨论了形如L（θ，δ）=（θ／δ）^q+（δ／θ）^q-2（q＞0）的q-对称熵损失下逆高斯分布形状参数的Bayes估计，并探讨了形如（cT+d）^-1的一类估计的容许性问题．结论部分，对本文的工作做以概括总结，并提出了有待改进和进一步探讨的研究方向．更多还原

【Abstract】 The symmetric loss function is of great importance in the theory of statistical decision, such as squared loss function, which refleCtS the fact that if an action is close to, then the decision is reasonable and little loss is incurred. If is far from, then a large loss is incurred and therefore is not good. In fact, the admissibility of the estimator may depend quite sensitively on features of the loss function. So it is important to do more study of the properties of alternative estimators relative to other types of symmetric loss function. This paper deals with Bayes estimator for the shape parameter of inverse Gauss distribution when the mean parameter is known under the q- symmetric entropy joss, and discusses the admissibility and inadmissbility of estimator with the form of （cT+d）^-1.The first part of the article give a brief introduction of inverse Gauss distribution; The second part of the article give a brief account of the back ground of the theory of statistical decision and Bayes decision, the concept of admissibility and inadmissibility, and so on. Part three deals with Bayes estimator for the shape parameter of inverse Gauss distribution when the mean parameter is known under the q- symmetric entropy joss, and discusses the admissibility and inadmissbility of estimator with the form of （cT + d）^-1. Conclusion of this work is done to conclude the estimation method, moreover we discuss the feasibility and what we have to improve and explored in deep research.更多还原