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

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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