2009 Fiscal Year Final Research Report
Study on construction and applications of high-dimensional information criteria
| Project/Area Number |
19500243
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | Chuo University |
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Principal Investigator |
FUJIKOSHI Yasunori Chuo University, 理工学部, 客員教授 (40033849)
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| Co-Investigator(Kenkyū-buntansha) |
SUGIYAMA Takakazu 中央大学, 理工学部, 教授 (70090371)
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| Co-Investigator(Renkei-kenkyūsha) |
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) |
2007 – 2009
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| Keywords | 高次元情報量基準 / 多変量モデル / 判別分析 / 変数選択 / 高次元小標本 / 正準相関 / 経時データモデル / 共分散構造 |
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| Research Abstract |
In this study, we considered to derive model selection criteria for various multivariate models under high-dimensional situations where the dimension is smaller than the sample size, but both of them tend to infinity. Concretely we derived high-dimensional AIC for additional information models in discriminant analysis, CAIC criterion for parallelism models in MANOVA and modified Cp criterion for selection of ridge parameters in multivariate regression model. Further, we derived high-dimensional asymptotic distributions of the roots in MANOVA, canonical correlations, etc.
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