2002 Fiscal Year Final Research Report Summary
A study of the development of asymptotic theory in multivariate analysis and its applications
| Project/Area Number |
12440028
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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 | HIROSHIMA UNIVERSITY |
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Principal Investigator |
FUJIKOSHI Yasunori Hiroshima Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (40033849)
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| Co-Investigator(Kenkyū-buntansha) |
WAKAKI Hirofumi Hiroshima Univ., Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (90210856)
NISHII Ryuei Hiroshima Univ., Faculty of Integrated Arts and Sciences, Professor, 総合科学部, 教授 (40127684)
OHTAKI Megu Hiroshima Univ., Research Institute for Radiation Biology and Medicine, Professor, 原爆放射線医科学研究所, 教授 (20110463)
FUJIOKA Teruo Hiroshima Univ., Graduate School of Science, Research Assistant, 大学院・理学研究科, 助手 (50221544)
SEO Takashi Science Univ. of Tokyo, Faculty of Science, Lecturer, 理学部, 講師 (00266909)
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| Project Period (FY) |
2000 – 2002
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| Keywords | asymptotic theory / multivariate analysis / asymptotic exapansion / MANOVA tests / AIC criterion / growth curve model / nonparametric regression / remote sensing data |
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| Research Abstract |
The purpose of this project is to develop statistical asymptotic theory in multivariate methods and its applications. The main results are as follows: 1. We derived asymptotic expansions of the distributions of some basic statistics and typical three statistics in one-way MANOVA and multivariate linear models (Fujikoshi(2002), Wakaki, Yanagihara and Fujikoshi(2002)). 2. For the problem of obtaining error bounds for asymptotitc expansions, we derived error bounds for Hotelling's T^2_0 and Wilks Lamnda (Technical Reports: Fujikoshi, Ulyanov and Shimizu(2002), Fujikoshi and Ulyanov(2003)). 3. Developing asymptotic theory in a high dimensional framework, we proposed a criterion for variables of selection in discriminant analysis (Fujikoshi(2002)). 4. In anlalysis of growth curve models with hierachical within-individual design matrices, we proposed an improved AIC criterion (Fujikoshi(2002)), and a method of constructing simultaneous confidence regions (Yanagihara and Ohtaki (2002)). 5. Related to a fitting problem in nonparametric regression, we proposed a method (Satoh,. Yanagihara and Otaki(2002)) of combining B-spline and polynomial regressions, and a method (Yanagihara and Ohtaki(2002)) of optimizing knots-placement to avoid over fitting in B-spline scedastic smoothing. 6. We wrote chapters 2; 「Landsat Data」 (Nishii, Tanaka and Itakura(2002)) in the book 「Earth Environmental Data」 (Shimizu, K., ed.). Further, we proposed a method (Nishii(2002)) of discriminating land-cover categories based on multivariate geo-spatial data observed by artificial satellites or airborne sensors. 7. We proposed a method (Fujioka and Yanagimoto(2001)) of estimating the normal mean vector whose norm is known.
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