Grant-in-Aid for Scientific Research (A)
General mathematics (including Probability theory/Statistical mathematics)
|Research Institution||Chiba University|
TAGURI Masaaki Chiba Univrsity, Faculty of Science, Professor, 理学部, 教授 (10009607)
蔵野 正美 千葉大学, 教育学部, 教授 (70029487)
安芸 重雄 大阪大学, 基礎工学部, 助教授 (90132696)
長尾 壽夫 大阪府立大学, 工学部, 教授 (80033869)
谷口 正信 大阪大学, 基礎工学部, 助教授 (00116625)
YANAGAWA Takashi Kyushu University, Graduate School of Mathematics, Professor, 大学院・数理学研究科, 教授 (80029488)
久保川 達也 東京大学, 経済学部, 助教授 (20195499)
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)
椿 広計 筑波大学, 大学院・経営システム科学研究科, 助教授 (30155436)
KUSHIMOTO Shigeru Kanazawa University, Faculty of Education, Professor, 教育学部, 教授 (90020114)
|Project Fiscal Year
1996 – 1997
Completed(Fiscal Year 1997)
|Budget Amount *help
¥17,800,000 (Direct Cost : ¥17,800,000)
Fiscal Year 1997 : ¥8,900,000 (Direct Cost : ¥8,900,000)
Fiscal Year 1996 : ¥8,900,000 (Direct Cost : ¥8,900,000)
|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 / 複雑非線形現象の統計解析 / 多変量解析と漸近理論 / 数理計画モデルの最適化 / 時系列解析と漸近理論 / 逐次統計解析 / 確率分布論・統計的推測理論 / 計算機統計 / 統計モデル論 / 推定方程式 / 統計的漸近理論 / 統計モデル / 統計的推定論 / 複雑非線形現象 / 離散・ノンパラ・セミパラ解析 / 多変量解析 / 数理計画モデル / 時系列解析 / 確率分布論|
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.