Researches on the Non-Regular Inference Theory and the Concepts of the Amounts of Information

(2)在统计非正则理论中，讨论了估计量的性质，得到了关于非正则分布的刻画的新知识。(3)在推理论及其信息论观点中，通过信息量阐明了推理的结构，并研究了其与信息论的关系。(4)在分析先验信息统计模型及其应用的基础理论中，从贝叶斯的角度考虑了推理过程的最优性，得到了将其应用于实际问题的可能性的结果。(5)详细研究了多元分析与时间序列之间的空间，并在…上得到了新的结果(6)在组合设计及其应用中，提出并评价了实验设计的结构。(7)在经济时间序列和数学金融中，尝试了统计推理基本理论的构建，并考察了其实用性。(8)在多元分析中，讨论了线性和非线性模型，并在非正则情形下得到了新的推断结果。(9)从序贯分析的角度研究了统计推理的理论基础及其应用。在统计和数学分析中，给出了关于估计和检验过程效率的新结果。此外，还得到了统计建模和推断、空间统计学、计算机辅助类型推理及其应用等方面的新结果。就此举行了多次座谈会，并进行了积极的讨论和信息的相互交流。他们的结果被总结成一本大约800页的书。较少

The statistical investigation on various themes was done as follows.(l)0n the statistical inference and its related topics, the inferential procedures were proposed and interesting results on the application were obtained.(2)0n the statistical non-regular theory, the properties of estimators were discussed, and new knowledges of the characterization of non-regular distributions were obtained.(3)0n the theory of inference and its information theoretic viewpoint, the structure of inference was clarified through amounts of information, and its relation to the theory of information was well investigated.(4)0n the fundamental theory to analyze the statistical model with prior informations and its applications, the optimality of inferential procedures was considered from the Bayesian point of view, and the results on possibility of the application to practical problems were obtained.(5)The space between multivariate analysis and time series was investigated in details, and new results on the … More comparison of inferential procedures were given.(6)0n the combinatoric design and its applications, the construction of experimental design was proposed and assessed.(7)0n the economic time series and mathematical finance, the construction of the fundamental theory of statistical inference was tried and its usefulness is investigated.(8)0n the multivariate analysis, the linear and non-linear models were discussed, and new results on the inference were obtained in the non-regular case which was regarded as a difficult one.(9)The theoretical fundamentals and its applications were well investigated from the viewpoint of sequential analysis, and new results on the inferential procedures were obtained in the case of non-regular distributions.(10)0n the statistical and mathematical anakysis, new results on the efficiency of estimation and test procedures were given.In addition to the above, the results on the statistical modeling and inference, the spatial statistics, the recent computer-assisted type inference and its applications and others were also obtained. Many symposiums on the above were held and active discussions and mutual exchanges of informations were also done. Their results were summarized as a book of about 800 pages. Less