Research on the mathematical structure of statistical inference and its application

统计学的一个常用方法是通过对真实的领域中的实际问题的数学结构的深入理解来发展统一的理论。另一方面，在应用上，理论应该被修改以满足它所应用的真实的领域所固有的各种限制。它们的统一和规范在发展统计理论中是必不可少的。本研究特别关注这种理论与应用之间的相互作用，并已成功地完成，获得了大量的理论和方法的结果，所做的理论工作是：1新的估计理论，检验和渐近的基础上的几何结构的统计推断。2新的设计理论和试验分析，包括正交试验、平衡试验和一些不完全区组设计。3正随机变量的非正态连续分布理论，如集中度分布， 关于我们 on，the price价格and the survival生存data数据. 4非平稳和非线性时间序列的新方法。5多元分析的新方法论，包括多元回归分析和多维标度。某些特定领域固有的应用工作是1工业中与其快速发展的技术和新数学以及公司的新概念相对应的新方法论-广泛的质量控制，强调在早期阶段，如规划或设计，而不是在制造或检查过程中创造一个有吸引力的质量。2.医学上的新方法论，其特点是不同研究对象之间的测量偏差很大，在重复观察中很难保持环境不变，还有许多不完整的观察。3空间统计理论在地震学、地质学和破坏物理学中的应用。最后得到了统计计算中的一些有用结果，包括平滑技术和恢复过程。少

It is usual approach of statistics to develop a unified theory through a deep insight into the mathematical structure abstracted from to practical problems in a real field. On the other hand on application the theory should be modified to meet various restrictions intrinsic to the real field which it its applied. Their unification and specification is essential in developing a statistical theory. This research in particularly concerned with this sort of interactions between theory and application and has been successfully fulfilled to obtained a large number of theoretical and methodological result.The theoretical works performed are 1 New theory of estimation, tests and asymptotics based on the geometrical structure of the statistical inference.. 2 New theory of design and analysis of experiments including the orthogonal array, the balanced array and some incomplete block designs. 3 Theory of nonnormal continuous distributions for positive random variables such as from the concentrati … More on, the price and the survival data. 4 New methodology for a nonstationary and nonlinear time series. 5 New methodology for the multivariate analysis including the multiple regression analysis and the multidimensional scaling.Applied works intrinsic to some particular field are 1 New methodology in the industry corresponding to its quick development technique and in new mathematics and also to the new concept of company-wide quality control which emphasize creating an attractive quality in earlier stage such as planning or design rather than in manufacturing or inspection processes. 2 New methodology in medicine which is characterized by the large deviations of measurement from subject to subject, by the difficulty of keeping circumstances constant in repeating observations and also by many sorts of incomplete observations. 3 Application of theory of spatial statistics to seismology, geology and to destruction physics. Finally we got some useful results in statistical computing including smoothing techniques and resampling procedures. Less