Research on the mathematical structure of statistical inference and its application

统计学的通常方法是通过对从实际领域中的实际问题抽象而来的数学结构的深刻洞察来发展一个统一的理论。另一方面，在应用上，理论应加以修改，以满足其应用的实际领域所固有的各种限制。它们的统一和规范对于发展统计理论是必不可少的。这项研究特别关注这种理论与应用之间的相互作用，并已成功地完成了大量的理论和方法结果。所做的理论工作是：1基于统计推理的几何结构的估计、检验和渐近的新理论。2实验设计和分析的新理论，包括正交表、平衡表和一些不完全区组设计。3正态随机变量的非正态连续分布理论，如来自集中…更多的是，价格和生存数据。4非平稳、非线性时间序列的新方法。5多变量分析的新方法，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行业中与其快速发展的技术和新数学相对应的新方法，以及强调在早期阶段(如规划或设计)而不是在制造或检验过程中创造有吸引力的质量的公司范围内的质量控制的新概念。2医学新方法论，其特点是不同学科之间的测量偏差很大，在重复观察时很难保持环境恒定，而且还存在多种不完整的观察。3空间统计学理论在地震学、地质学和破坏物理学中的应用。最后，我们在统计计算中得到了一些有用的结果，包括平滑技术和重采样过程。较少

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