| Project/Area Number |
05452014
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| Research Category |
Grant-in-Aid for General Scientific Research (B)
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| Allocation Type | Single-year Grants |
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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 Yasunoro Hiroshima Univ., Mathematics, Professor, 理学部, 教授 (40033849)
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| Co-Investigator(Kenkyū-buntansha) |
TAKENAKA Shigeo Hiroshima Univ., Associate Professor, 理学部, 助教授 (80022680)
KUBO Izumi Hiroshima Univ., Professor, 理学部, 教授 (70022621)
WATAMORI Yoko Hiroshima Univ., Research Assistant, 理学部, 助手 (70240538)
FUJIOKA Teruo Hiroshima Univ., Research Assistant, 理学部, 助手 (50221544)
SASABUCHI Syoichi Hiroshima Univ., Mathematics, Associate Professor, 理学部, 助教授 (20128028)
草野 尚 広島大学, 理学部, 教授 (70033868)
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| Project Period (FY) |
1993 – 1994
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| Project Status |
Completed (Fiscal Year 1994)
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| Budget Amount *help |
¥5,600,000 (Direct Cost: ¥5,600,000)
Fiscal Year 1994: ¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 1993: ¥3,100,000 (Direct Cost: ¥3,100,000)
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| Keywords | Multivariate nonnormal models / Statistical inference / Multivariate analusis of variance / Canonical correlation model / Lagevin distribution / Inequality restriction / Semi-parametric regression model / Robustness / セミパラメトリック回帰モデル / 多変量1元配置モデル / 回帰モデル / ノンパラメトリック推定 / ロバスト推定 / 経時データ解析 |
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| Research Abstract |
Research results of this projects can be divided roughly into the following three categories :
1. First, to study how effective the statistical procedures proposed under multivariate normal models are under multivariate nonnormal models, and next, to develop the statistical procedures applicable for more general situations.
2. To develop the statistical procedures in some speficic multivariate nonnormal models.
3. Research on related topics in statistic and mathematics.
Related to the first category, Y.Fujikoshi studied on some multivariate test statistics and latent roots in multivariate analysis of variance, and aucceeded to obtain some new results under elliptical distributions and a general distribution involving continuous distributions.
Related to the second category, Y.Watamori developed higher order asymptotic theory of statistical inference on Langevin distribution, and explored instrinsic approach of statistical distributions on a sphere. S.Sasabuchi made a comparative study of several tests for the equality of several binomial populations with ordered restrictions. T.Fujioka gave an exiplicite expression for the estimator of variance based on minimax approach in semi-parametric regression model, and studied its properties.
Related to the third category, we obtained new results on various areas : Y.Fujikoshi 「statistical inference of repeated measurements and its applications and error bounds for asymptotic expansions of distributions」 , S.Sasabuchi 「statistical inference of multivariate normal distributions with ordered restrictions」 , I.Kubo, S.Takenaka and M.Nakamura 「probability Theory」 , T.Kusano, M.Mimura and M.Naito 「Analysis」 , A.Kowata 「Geometry」 .
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