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

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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