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Developments of Accurate Estimation Procedures in the Statistical Region Estimation and Attempt of Practicability

统计区域估算中精确估算程序的发展及实用性尝试

基本信息

批准号：
12554002
负责人：
AKIHIRA Masafumi
金额：
$ 8.77万
依托单位：
University of Tsukuba
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2003
项目状态：
已结题

项目摘要

The investigation on various themes was systematically done, in cooperation with researchers in related areas to statistical region estimation, as follows. (1) On the development of procedures, in the experimental design and its periphery, and the application, interesting results are obtained. (2) On the development of procedures on statistical region estimation and its application are closely studied. (3) The theory of computer-oriented statistical procedures and its application are examined in detail, new knowledge on the comparison of estimation procedures is obtained, and more accurate procedures are developed. (4) The resolution of the combinatorial structure of experimental design and its periphery and the application are closely studied, the procedures are developed, and practically useful procedures are investigated. In particular, in the experimental physics etc., there are many cases where a parameter is essentially assumed to be theoretically positive (or nonnegative} valued … More . Then there is a problem to make an interval estimation of an unknown parameter from the observation with errors. If the errors have the same magnitude as the value of the unknown parameter, then the ordinary confidence interval involves a negative part since it disregards that the parameter is positive valued, and the interval can be an empty set provided that the parameter is restricted to be positive. On the problem physicists proposed many ways to construct confidence intervals, but from the viewpoint of statistical region estimation, there are Bayesian and non-Bayesian angles. In the Bayesian case, it is enough to confine the prior distribution to the region of the existence of the parameter. In the investigation, the combined Bayesian-frequentist approach is proposed to construct the confidence interval for a restricted parameter. Comparing the method with usual pivotal and likelihood ones, it is examined to be reasonable. And a research toward the practice by the new method is also done Less

与统计区域估计相关领域的研究人员合作，对各种主题进行了系统的调查，如下所示。(1)在程序的开发上，在实验设计及其外围，以及应用方面，取得了有趣的结果。(2)对统计区域估计程序的发展及其应用进行了深入研究。(3)详细研究了面向计算机的统计程序的理论及其应用，对估计程序的比较有了新的认识，开发了更精确的程序。(4)对试验设计及其外围的组合结构的求解及其应用进行了深入的研究，开发了相应的程序，并研究了实用的程序。具体地，在实验物理等中，存在许多情况，其中参数基本上被假定为理论上正的(或非负的)值…更多。然后，存在着从有误差的观测中对未知参数进行区间估计的问题。如果误差具有与未知参数的值相同的大小，则普通的置信度区间涉及负部分，因为它忽略了该参数是正值的，并且该区间可以是空集，只要该参数被限制为正值。在这个问题上，物理学家提出了许多构造可信区间的方法，但从统计区域估计的角度来看，有贝叶斯和非贝叶斯两种角度。在贝叶斯的情况下，将先验分布限制在参数存在的区域就足够了。在研究中，提出了用贝叶斯-频域相结合的方法来构造约束参数的置信度区间。将该方法与常用的关键方法和似然方法进行比较，验证了该方法的合理性。而将新方法应用于实践的研究也较少。