| Project/Area Number |
13440034
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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 |
KONISHI Sadanori KYUSHU UNIVERSITY, Faculty of Mathematics, Professor, 大学院・数理学研究院, 教授 (40090550)
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| Co-Investigator(Kenkyū-buntansha) |
HYAKUTAKE Hiroto KYUSHU UNIVERSITY, Faculty of Mathematics, Associate Professor, 大学院・数理学研究院, 助教授 (70181120)
UCHIDA Masayuki KYUSHU UNIVERSITY, Faculty of Mathematics, Associate Professor, 大学院・数理学研究院, 助教授 (70280526)
MAESONO Yoshihiko KYUSHU UNIVERSITY, Faculty of Economics, Professor, 大学院・経済学研究院, 教授 (30173701)
YANAGAWA Takashi Kurume University, Bio-statistics center, Director general, バイオ統計センター, 教授 (80029488)
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| Project Period (FY) |
2001 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥11,700,000 (Direct Cost: ¥11,700,000)
Fiscal Year 2004: ¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 2003: ¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 2002: ¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 2001: ¥3,100,000 (Direct Cost: ¥3,100,000)
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| Keywords | Nonlinear modeling / Bayesian model selection criterion / Radial basis function / Classification and Discrimination / Functional data analysis / Nonlinear time series analysis / Diffusion process / Regularized basis expansions / 非線形基底展開 / ノンパラメトリックグラフィカルモデリング / 統計的因果関係 / 統計的漸近理論 / 繰り返し測定値 / 基底関数展開法 / 非線形構造解析 / グラフィカルモデリング / カオス的時系列 / L-統計量 / 非線形判別 / 高次元データ解析 / ニューラルネットワーク / 超過変動 / 多重比較 / 漸近理論 / 情報量規準 / バイオ統計学 / 複雑非線形データ解析 / ブートストラップ |
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| Research Abstract |
In recent years the wide availability of fast and inexpensive computers enables us to accumulate a huge amount of data, and the effective use of databases are required in order to create innovation and values and to solve important science and engineering problems. Statistical challenges posed by large data sets arise in such areas as genome databases in life science, remote-sensing data from earth observing satellites, POS data in marketing and economic data. Through this research project we have investigated the problem of constructing various types of statistical nonlinear modeling strategies and obtained the results in the following :
(1)We proposed nonlinear modeling techniques ; determining a set of basis functions, estimating the unknown parameters by regularization and then evaluating the constructed model to select a suitable one among competing models. We describe modeling based on functional approach and introduce a generalized information criterion. Bayesian information criterion BIC is also extended in such a way that it can be applied to the evaluation of models estimated by the method of regularization.
(2)We proposed functional regression modeling and functional discriminant analysis, using Gaussian radial basis functions along with the technique of regularization. The proposed method was applied to the analysis of yeast cell cycle gene expression data.
(3)Approximate selection of embedding dimension and delay time have been a central issue of chaotic dynamical systems. We introduced the delay time and consider the estimation of embedding dimension and delay time.
(4)Model selection criteria were presented for stochastic process from an information-theoretic approach. We derived asymptotic expansions for the distributions of statistics related to small diffusions and applied it to option pricing in economics.
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