Variable selection methods in high-dimensional multivariate models and their applications
| Project/Area Number |
16K00047
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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 |
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| Co-Investigator(Kenkyū-buntansha) |
櫻井 哲朗 公立諏訪東京理科大学, 共通・マネジメント教育センター, 講師 (60609741)
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 多変量回帰モデル / 変数選択法 / 主成分分析 / 判別分析 / 情報量規準 / 一つ取って置き法 / 高次元漸近枠組 / 多変量モデル / 高次元漸近的枠組 / １つ取って置き法 / 共分散構造 / モデル選択規準 / 高次元多変量モデル / 高次元一致性 / 検定型変数選択規準 / 高次元漸近分布 / 成長曲線モデル / 統計数学 |
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| Outline of Final Research Achievements |
In multivariate analysis, especially, discriminant analysis, multivariate regression models, principal component analysis, canonical correlation analysis, etc., we derived sufficient conditions for consistency of variable selection methods based on information criteria when the sample size and the dimension are large. The methods have a computational problem when the number of variables are large. In order to avoid its computational problem, we proposed a generalized kick-one-out (KOO) method which shared the high-consistency property in discriminant analysis and multivariate regression model. Further, in the problem of rank estimation in multivariate linear model, we proposed a regularized information criterion,
which can be used for the case that the sample size is smaller then the dimension of variables, and studied its high-dimensional properties.
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| Academic Significance and Societal Importance of the Research Achievements |
多変量解析においては情報が入手しやすくなったこともあって, 変数の次元が大きい場合の統計的方法や, 膨大な変数の中から有用な変数を抽出する変数選択法に高い関心がよせられている. 本研究は, このような高次元データ分析における重要な課題における基礎的研究のみならず応用に焦点を当てており, 統計科学分野における理論や応用に関して高い貢献が期待される.
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Report
(4 results)
Research Products
(21 results)
