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

与统计区域估计相关领域的研究人员合作，系统地完成了对各个主题的调查，如下。 (1)在程序开发、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开发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，获得了有关估计程序比较的新知识，并开发了更准确的程序。 (4)深入研究实验设计及其外围组合结构的解析和应用，开发程序，研究实用程序。特别是在实验物理等领域，很多情况下参数本质上被假定为理论上正值（或非负值）。然后就存在一个问题，即根据观测值对未知参数进行带有误差的区间估计。如果误差与未知参数的值具有相同的大小，则普通置信区间会包含负部分，因为它忽略了参数的正值，并且只要参数被限制为正值，区间就可以是空集。物理学家提出了多种构建置信区间的方法，但从统计区域估计的角度来看，有贝叶斯角度和非贝叶斯角度，将先验分布限制在参数存在的区域就足够了。在研究中，提出了贝叶斯-频率组合方法来构建受限参数的置信区间，并通过与通常的关键和似然方法的比较，检验了该方法的合理性。也做得更少

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