| Project/Area Number |
63530015
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
統計学
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| Research Institution | The Institute of Statistical Mathematics |
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Principal Investigator |
HIRANO Katuomi Inst. Statist. Math., Dept. Fund. Statist. Theory, Prof., 統計基礎研究系, 教授 (30000186)
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| Co-Investigator(Kenkyū-buntansha) |
NIKI Naoto Kyushu University, Faculty of Sciences, Assoc. Prof., 理学部, 助教授 (10000209)
SHIMIZU Ryoichi Inst. Statist. Math., Dept. Fund. Statist. Theory, Prof., 統計基礎研究系, 教授 (10000192)
KONISHI Sadanori Inst. Statist. Math., Dept. Fund. Statist. Theory, Assoc. Prof., 統計基礎研究系, 助教授 (40090550)
安芸 重雄 統計数理研究所, 統計基礎研究系, 助手 (90132696)
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| Project Period (FY) |
1988 – 1990
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| Project Status |
Completed (Fiscal Year 1990)
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| Budget Amount *help |
¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 1990: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1989: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1988: ¥800,000 (Direct Cost: ¥800,000)
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| Keywords | Nonparametric methods / Multivariate analysis / Bootstrap methods / Scale mixture of multivariate random vector / Asymptotic expansions / Discrete distributions / Confidence intervals / Familial data / ノンパラメトリック統計手法 / ブ-トストラップ / スケ-ル分布族 / 多変量尺度混合 / リサンプリング / ナイル河問題 / ブートストラップ / 数式処理 |
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| Research Abstract |
The purpose of the research is to investigate the nonparametric statistical procedures in multivariate analysis. The followings are the main results obtained through this research project extending over three years.
1. Inference procedures for the intraclass and interclass correlations were investigated in the multivariate context of familial data, for which measurements are taken on several characteristics. Multivariate measures of interclass and intraclass correlations were proposed to assess the degree of resemblances among family members with respect to more than one characteristic. Unified estimators for the multivariate measures were proposed as the eigenvalues of certain random matrices constructed by the matrices of the weighted sums of squares and products of observations.
2. Asymptotic expansions were derived for the distributions of the scale mixtures of a multivariate random vector. Their error bounds were also obtained. The results were applied to the asymptotic distribution of the MLE in a general MANOVA model.
3. Properties of some discrete distributions were investigated. It was also discussed how to calculate maximum likelihood estimates of parameters of the discrete distributions of order k.
4. The problem of constructing approximate confidence intervals for functional parameters was considered in a nonparametric model. A unified approach to a normalizing transformation theory was provided, and the result was used to construct confidence intervals with second order accuracy. The relationship between the bootstrap methods and the proposed procedure was also investigated.
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