| Project/Area Number |
63302006
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| Research Category |
Grant-in-Aid for Co-operative Research (A)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | The University of Tokyo |
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Principal Investigator |
HIROTSU Chihiro Univ. of Tokyo, Fac. of Tech., Professor, 工学部・計数工学科, 教授 (60016730)
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| Co-Investigator(Kenkyū-buntansha) |
TANEMURA Masami Inst. of Statistical Mathematics, Associate Professor, 助教授 (80000214)
SIBUYA Masaaki Keio Univ., Fac. of Sci. and Tech., Professor, 理工学部, 教授 (20146723)
SHIBATA Ritei Keio Univ., Fac. of Sci. and Tech., Associate Professor, 理工学部, 助教授 (60089828)
KUDO Akio Kyushu Univ., Fac. of Sci., Professor, 理学部, 教授 (00037144)
KARIYA Takeaki Hitotsubashi Univ., Inst. of Economic Research, Professor, 経済研究所, 教授 (70092624)
宮川 雅巳 東京理科大学, 理工学部, 講師 (90157595)
清水 良一 統計数理研究所, 教授 (10000192)
竹村 彰通 東京大学, 経済学部, 助教授 (10171670)
藤井 光昭 東京工業大学, 理学部, 教授 (70016343)
柳川 堯 九州大学, 理学部, 助教授 (80029488)
影山 三平 広島大学, 学校教育学部, 助教授 (70033892)
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| Project Period (FY) |
1988 – 1989
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| Project Status |
Completed (Fiscal Year 1989)
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| Budget Amount *help |
¥13,100,000 (Direct Cost: ¥13,100,000)
Fiscal Year 1989: ¥6,600,000 (Direct Cost: ¥6,600,000)
Fiscal Year 1988: ¥6,500,000 (Direct Cost: ¥6,500,000)
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| Keywords | 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 / 推論の幾何学的構造 / 漸近展開 / 頑健推定・検定・予測 / 寿命分布 / タグチメソッド / 空間統計学生物形態学 / 実験計画法として分散分析 / 農事試験 / 非線形・非ガウス平滑化法 / モンテカルロ法 / 医学データ解析 / 時系列漸近分布理論 / 非定常・非線形時系列 / 多変量解析法 |
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| Research Abstract |
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
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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
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