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Statistical estimation of non-regular case by Bayesian approach

贝叶斯方法对非常规情况的统计估计

基本信息

批准号：
22740053
负责人：
OHYAUCHI Nao
金额：
$ 2.66万
依托单位：
University of Tsukuba
依托单位国家：
日本
项目类别：
Grant-in-Aid for Young Scientists (B)
财政年份：
2010
资助国家：
日本
起止时间：
2010-04-01 至 2014-03-31
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22740053/
关键词：
切断分布族位置母数推定問題漸近情報量損失極値統計量 Pitman推定量切断指数分布漸近分散荷重推定量最尤推定量位置母数切断分布族情報量損失Ｐｉｔｍａｎ推定量漸近集中確率最小分散不偏推定量完備十分統計量整級数展開 Bayes推定量 Bayesリスク

项目摘要

In the estimation problem on a location parameter for a family of two-sided truncated distributions, we considered the case when each distribution's support is an interval and its density had positive values on the interval and differential coefficients at its endpoints. Then, it was shown that the second order asymptotic loss of information of the statistic consisting of extreme values and an asymptotically ancillary statistic vanished. On the other hand, from the Bayesian viewpoint, the best location equivariant estimator (Pitman estimator) is regarded as the generalized Bayes estimator which minimized the risk with respect to an improper uniform distribution and the quadratic loss. In the above estimation problem, we obtained the asymptotic concentration probability of the Pitman estimator and compared it with other location equivariant estimators.

在一类双边截断分布族的位置参数估计问题中，考虑了每个分布的支撑是一个区间，其密度在区间上为正值，且在端点处为微分系数的情形.然后证明了由极值和一个渐近辅助统计量组成的统计量的二阶渐近信息损失消失。另一方面，从贝叶斯的观点，最佳位置同变估计（皮特曼估计）被视为广义贝叶斯估计，最小化的风险，关于一个不适当的均匀分布和二次损失。在上述估计问题中，我们得到了皮特曼估计的渐近集中概率，并与其它位置同变估计进行了比较。