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

与统计区域估计有关领域的研究人员合作，系统地进行了各种主题的调查，调查内容如下：(1)在程序的开发、实验设计及其外围、应用等方面，都获得了有趣的结果。(2)深入研究了统计区域估计方法的发展及其应用。(3)详细研究了面向计算机的统计程序理论及其应用，获得了关于估计程序比较的新知识，并开发了更精确的程序。(4)深入研究了实验设计组合结构及其外围问题的解决方法和应用，开发了实验设计组合结构的解决方法，并探讨了实验设计组合结构的实际应用。特别是，在实验物理等中，有许多情况下，参数基本上被假设为理论上的正（或非负）值…更多。然后，从有误差的观测值中对未知参数进行区间估计。如果误差的大小与未知参数的值相同，则普通置信区间包含负的部分，因为它忽略了参数的正值，并且如果参数被限制为正值，则该区间可以是空集。物理学家提出了许多构造置信区间的方法，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。在贝叶斯情况下，将先验分布限制在参数存在的区域内就足够了。在研究中，提出了贝叶斯-频率组合方法来构造受限参数的置信区间。将该方法与常用的枢纽法和似然法进行了比较，证明了该方法的合理性。并对新方法的应用进行了研究

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