| Project/Area Number |
08304015
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Chiba University |
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Principal Investigator |
TAGURI Masaaki Chiba Univrsity, Faculty of Science, Professor, 理学部, 教授 (10009607)
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| Co-Investigator(Kenkyū-buntansha) |
SUZUKI Takeru Waseda University, School of Science and Engineering, Professor, 理工学部, 教授 (60047347)
KANAZAWA Mitsuyo Fukui University, Faculty of Education, Professor, 教育学部, 教授 (50029518)
TARUMI Tomoyuki Okayama University, Faculty of Environmental Science and Technology, Professor, 環境理工学部, 教授 (50033915)
KUSHIMOTO Shigeru Kanazawa University, Faculty of Education, Professor, 教育学部, 教授 (90020114)
YANAGAWA Takashi Kyushu University, Graduate School of Mathematics, Professor, 大学院・数理学研究科, 教授 (80029488)
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| Project Period (FY) |
1996 – 1997
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| Keywords | Statistical analysis of chaotic, nonlinear data / Multivariate analysis and its asymptotic theory / Mathematical programming model and its optimization / Time series analysis and its asymptotic theory / Sequential analysis / Distribution theory and statistical inference / Computational statistics / Statistical model theory |
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| Research Abstract |
In this research, we investigated the theory of information extraction in mathematical statistics and applied the results to various kinds of practical data-set. 11 special topics were selected and research sympojiums were held on each topic. As a result, new theories and methodologies were developed and useful knowledges were obtained in many practical fields. Statistical software were also constructed. Through discussions in sympojiums and meetings, further problems were pointed out. Main results obtained in 11 sympojiums were as follows :
(1) Development of the theories and methodologies for analyzing complicated nonlinear data and investigation on the limit in practical use.
(2) Research of descriptive statistics and statistical inference on multivariate analysis, and the understanding of their discrepancy.
(3) Development of optimization theories in mathematical programming and model construction for applying the results to practical problems.
(4) Investigation on asymptotic theory, large deviation theory, model selection in time series analysis and their application.
(5) Investigation on the theories and methodologies of sample sizes in sequential analysis required to carry out efficient statistical inference.
(6) Investigation on probability distributions and sampling distributions concerning various statistical models.
(7) Investigation on combinatorial mathematics, integral conditions and optimization in statistical model construction and inference.
(8) Development of the theories on computer-intensive statistical methods and construction of useful statistical software.
(9) Development of statistical asymptotic theory and construction of the computer-intensive algorithms.
(10) Investigation on statistical inference concerning multivariate model, stochastic process model, time siries model and Baysian model.
(11) Construction of good estimators and joint confidence intervals, and investigation on their properties.
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