| Project/Area Number |
21540114
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | The University of Tokyo |
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Principal Investigator |
KUBOKAWA Tatsuya 東京大学, 経済学研究科(研究院), 教授 (20195499)
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| Project Period (FY) |
2009-04-01 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 多変量解析 / 線形混合モデル / 小地域推定 / 統計的決定論 / バートレット補正 / 高次元解析 / 漸近不偏性 / ベイズ推測 / 統計的推測 / 予測分布 / 仮説検定 / 縮小推定 / ベンチマーク法 / 経験ベイズ推定 / 変数選択規準 / ベンチマーク問題 / 高次元多変量解析 / 線形判別関数 / ブートストラップ / 信頼区間 / 情報量規準 / 漸近展開 / 多変量回帰モデル / 変数選択 / 高次元問題 / リッジ推定 / ミニマックス性 / ベイズモデル / 高次漸近理論 / 予測誤差 |
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| Research Abstract |
In this research project, new procedures were derived in estimation, hypothesis testing, predction and variable selection in multivariate statistical models as well as theories for justfying the new procedures were developed. In particular, we treated problems, models or situations where conventional methods had drawbacks for use or were not available, and then we tried to derive and suggest procedures which could resolve the problems. Of these, the following multivatiate statistical issues were addressed and new theories were developed with applications: (1) higher order asymptotic corrections in mean squared errors and confidence intervals in small area estimation, (2) benchmark problems in small area estimation under continuous and discrete mixed models, (3) Bartlett corrections and methods for variable selection in linear mixed models, (4) high dimensional procedures in linear discrimination and (5) optimality in estimation of multi-dimensional parameters.
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