Research on the mathematical structure of statistical inference and its application

统计推断的数学结构及其应用研究

• 批准号: 63302006
• 负责人: HIROTSU Chihiro
• 金额: $ 8.38万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Co-operative Research (A)
• 财政年份: 1988
• 资助国家: 日本
• 起止时间: 1988 至 1989
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-63302006/
• 关键词: Geometrical structure of statistical inference; Design and analysis of experiments; Nonstationary and nonlinear time series; Robust estimation; Multivariate analysis; Company-wide quality control; Spatial statistics; Statistical computing; 推論の幾何学的

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

通过深入洞察从实际领域的实际问题中抽象出来的数学结构来发展统一的理论是统计学的常用方法。另一方面，在应用上，理论应该被修改，以满足其应用的实际领域固有的各种限制。它们的统一和规范对于统计理论的发展至关重要。这项研究特别关注理论与应用之间的这种相互作用，并已成功地取得了大量的理论和方法论成果。所完成的理论工作有： 1 基于统计推断的几何结构的估计、检验和渐近的新理论。 2 实验设计和分析的新理论，包括正交阵列、平衡阵列和一些不完全块设计。 3 正随机变量的非正态连续分布理论，例如集中度、价格和生存数据。 4 非平稳和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有 1 行业中的新方法，与其快速开发技术和新数学相对应，也与全公司质量控制的新概念相对应，该概念强调在规划或设计等早期阶段而不是在制造或检查过程中创造有吸引力的质量。 2 医学中的新方法论，其特点是受试者之间的测量偏差很大，重复观察中难以保持环境恒定，以及多种不完整的观察。 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，我们在统计计算方面得到了一些有用的结果，包括平滑技术和重采样程序。较少的

项目成果

Fujikoshi,Yasunori: Journal of Multivariate Analysis. 27. 194-205 (1988)

Fujikoshi，Yasunori：多元分析杂志。

Jimbo,Masaichi: "Optimal autheutication systems and combinatorial designs" IEEE Trans.on Information Theory(掲載予定). 36. (1990)

Jimbo, Masaichi：“最优认证系统和组合设计”IEEE Trans.on Information Theory（即将出版）36。

Takemura,Aakimichi: "Some results on univariate and multivariate Cornish-Fisher expansion:algebraic properties and validity" Sankhya. A50. 111-136 (1988)

Takemura，Aakimichi：“单变量和多元 Cornish-Fisher 展开的一些结果：代数性质和有效性”Sankhya。

Ohashi,Yasuo: "Application of permutation tests for cancer clinical traial data" Bull.Biometric Soc.Japan. 9. 117-121 (1988)

Ohashi，Yasuo：“癌症临床试验数据的排列测试的应用”Bull.Biometric Soc.Japan。

Kageyama,Sanpei: Bulletine of Faculty of Education,Hiroshima university. 11. 47-61 (1988)

影山三平：广岛大学教育学部通报。