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，对各种主题进行了系统的调查，具体如下。(1)在程序的开发、实验设计及其外围以及应用方面，获得了有趣的结果。(2)对统计区域估计及其应用程序的发展进行了深入研究。(3)面向计算机的统计程序及其应用的理论进行了详细的研究，获得了新的知识，估计程序的比较，更准确的程序开发。(4)对试验设计的组合结构的解析及其周边和应用进行了深入的研究，开发了程序，并研究了实际有用的程序。特别是在实验物理学等方面，在许多情况下，参数基本上被假定为理论上为正值（或非负值 关于我们 .然后，有一个问题，使一个未知参数的区间估计从误差的观察。如果误差与未知参数的值具有相同的幅度，则普通置信区间包含负部分，因为它忽略了参数是正值，并且如果参数被限制为正值，则该区间可以是空集。关于这个问题，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的角度。在贝叶斯情况下，将先验分布限制在参数存在的区域就足够了。在研究中，提出了贝叶斯-频率论相结合的方法来构造约束参数的置信区间。通过与常用的主元法和似然法的比较，验证了该方法的合理性。并对新方法在实践中的应用进行了探讨

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