| Project/Area Number |
18K11188
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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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| Review Section |
Basic Section 60030:Statistical science-related
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| Research Institution | The University of Tokyo |
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Principal Investigator |
Kubokawa Tatsuya 東京大学, 大学院経済学研究科(経済学部), 教授 (20195499)
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| Project Period (FY) |
2018-04-01 – 2024-03-31
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| Project Status |
Completed (Fiscal Year 2023)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2021: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 統計的決定理論 / 縮小推定 / 多変量解析 / 小地域推定 / ミニマックス性 / 高次元解析 / ベイズ推定 / 線形混合モデル / スタイン問題 / 歪正規分布 / 高次元統計 / 推測統計 / 混合効果モデル |
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| Outline of Final Research Achievements |
In this research project, various inference problems were addressed regarding three topics: (A) new developments in small area estimation theory using mixed effects models, (B) new developments in the Stein problem concerning simultaneous estimation of multidimensional parameters, and (C) the effectiveness and usefulness of shrinkage estimation methods in high-dimensional multivariate models. Theoretical properties regarding the effectiveness and optimality and the usefulness from an applied perspective were investigated.
In particular, a new theory of small area estimation incorporating skew-normal distribution as the distribution of random effects was developed and its usefulness was demonstrated through data analysis. Additionally, a new challenge of simultaneous estimation of mean vectors in skew-normal distributions and derivation of conditions for minimaxity of shrinkage estimators were addressed.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究課題では，統計的決定理論と小地域推定理論に関する様々なトピックについて新たな理論の構築と応用での有用性が示されており，これらの分野への理論研究の貢献を与えている。特に，歪んだ正規分布やランク落ちした共分散行列などを組み込んだ新たなモデルの提案と新たな推測手法の導出は挑戦的な取り組みであり，これらの分野の次のステップへの貢献に繋がる。また，小地域推定は官庁統計・政府統計において重要な分野であるので，数理統計学からの新たな理論的な貢献は応用的にも意味があると考えられる。
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