| Project/Area Number |
09440083
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| Research Category |
Grant-in-Aid for Scientific Research (B).
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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 | KYUSHU UNIVERSITY |
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Principal Investigator |
YANGAWA Takashi Faculty of Mathematics, KYUSHU UNIVERSITY, Prof., 大学院・数理学研究院, 教授 (80029488)
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| Co-Investigator(Kenkyū-buntansha) |
OHTAKI Megu Hiroshima Univ., Research Inst of Radiation Medcine, Prof, 原爆放射能医学研究所, 教授 (20110463)
TAGURI Masaaki Chiba Univ., Faculty of Science, Prof., 理学部, 教授 (10009607)
KONISHI Sadanori Faculty of Mathematics, KYUSHU UNIVERSITY, Prof., 大学院・数理学研究院, 教授 (40090550)
FUEDA Kaoru Faculty of Mathematics, KYUSHU UNIVERSITY Ass, 大学院・数理学研究院, 助手 (50253399)
KAKIZAWA Yoshihide Hokkaido Univ., Faculty of Economics, Ass.Prof., 大学院・経済学研究科, 助教授 (30281778)
越智 義道 大分大学, 工学部, 助教授 (60185618)
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| Project Period (FY) |
1997 – 2000
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| Project Status |
Completed (Fiscal Year 2000)
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| Budget Amount *help |
¥12,600,000 (Direct Cost: ¥12,600,000)
Fiscal Year 2000: ¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 1999: ¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 1998: ¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 1997: ¥3,900,000 (Direct Cost: ¥3,900,000)
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| Keywords | bootstrap / etra binomial distribution / extra Poisson distribution / observational chaos / information criterion / generalized nonlinear model / Lyapunov exponent / nonlinear autoregressive model / 非線形因果解析 / bioassay / カテゴリカルデータ / 情報量規準 / 非線形時系列 / 交叉検証法 / スプライン近似 / 埋め込み次元 |
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| Research Abstract |
・A method of estimating embedding dimension and delay time is developed, and the usefulness of the method is demonstrated by analysing pulsasion data and EEG data
・An estimator for the Lyapunov exponent is developed in a framework of nonlinear autoregressive model and its consisitency is proved
・Universal method is developed for evaluating estimated logistic model with penaluty term, and its usefulness is prove by simulation
・A method of evaluating Bayesian prediction model is developed based on information criterion, and th method is successfully applied to estimation of hyper parameter
・Statistical tests are developed for the bootstrap method. Also usefulness of the bootstrap method in estimating variance for estimators in nonlinear complex situation
・An algorithm is developed for computing nonlinear optimization problems based on new idea of cross-excange conditional expectation, and also computer program is developed
・Efficiency of Bahadur slope is proved in a framework of stationary time series
・Asymptotic normality of Cross-varidation estimator for mean square error in prediction is proved
・Nonlinear trend tests are developed for data that show extra Poisson and extra Binomial dispersion
・Mantel-Haenszel type estimators for relative risk are developed in counter-mached sampling design and also for hazard rates in survival analysis
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