High-Dimensional Statistical Inference for Multivariate Models and Its Applications
| Project/Area Number |
25330038
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | Hiroshima University |
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Principal Investigator |
Fujikoshi Yasunori 広島大学, 理学(系)研究科(研究院), 名誉教授 (40033849)
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| Co-Investigator(Kenkyū-buntansha) |
YANAGIHARA HIROKAZU 広島大学, 大学院理学研究科, 准教授 (70342615)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 多変量線形モデル / 多変量回帰モデル / 判別分析モデル / 成長曲線モデル / 変数選択法 / モデル選択規準 / 高次元性一致性 / 冗長性検定 / 主成分分析 / 正準相関分析 / 情報量規準 / 高次元漸近的枠組 / 規準量の一致性 / 高次元漸近分布 / 変数選択 / AIC規準 / Cp規準 / 高次元漸近的枠 |
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| Outline of Final Research Achievements |
In this project we derived high-dimensional consistency properties for variable selection methods based on model selection criteria in multivariate linear model including multivariate regression model and discriminant analysis and in growth curve model. The model selection criteria treated includes AIC criterion, BIC criterion and Cp criterion. The high-dimensional properties were derived under a high-dimensional asymptotic framework such that the ratio of the number of response variables to the sample size tends to a fixed number less than 1. Further, we derive a high-dimensional asymptotic distribution for the likelihood ratio criterion for testing an additional information hypothesis in canonical correlation analysis and its error bound.
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Report
(4 results)
Research Products
(25 results)
