2004 Fiscal Year Final Research Report Summary
Mathematical modeling for high-dimensional nonlinear data and its application to the analysis of complex phenomena
| 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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| 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 |
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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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[Journal Article] Neural network nonlinear regression modeling and Information Criteria2001
Author(s)
Ando, T., Konishi, S.
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Journal Title
Advances in Statistics, Combinatorics and Related Areas (Gulati, C., Lin Y.-X., Mishra, S., Rayner, J.Eds.)(World Scientific)
Pages: 11-22
Description
「研究成果報告書概要(欧文)」より
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[Book] 情報量規準2004
Author(s)
小西 貞則, 北川 源四郎
Total Pages
194
Publisher
朝倉書店
Description
「研究成果報告書概要(和文)」より
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