Research on derivations of Bayes estimators with decision-theoretical optimality and their applications
| Project/Area Number |
16500172
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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 | The University of Tokyo |
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Principal Investigator |
KUBOKAWA Tatsuya The University of Tokyo, Graduate School of Economics, Professor (20195499)
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| Project Period (FY) |
2004 – 2007
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| Project Status |
Completed (Fiscal Year 2007)
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| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2006: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2005: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2004: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | Bayesian method / statistical decision theory / minimaxity / hierarchical Bayes model / linear mixed model / small area estimation / parametric restriction / variance component / 経験ベイズ推定 / 情報量規準 / 信頼区間 / F検定 / 高次元解析 / 判別分析 / 階層的ベイズ推定 / 線形回帰モデル / 変数選択 / 共分散行列 / 一般化ベイズ推定 / ミニマクス性 / 許容性 / 高次元データ / 統計的決定理論 / 変量効果モデル / 経験ベイズ |
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| Research Abstract |
The usefulness of the Bayesian procedures has been recently recognized from practical aspects. In this research project, I have shown the optimality of the Bayesian procedures from a decision-theoretic view point in several statistical problems as well as the usefulness in applications. The details are given below:
1) In the estimation of a mean vector of a multivariate normal distribution, the characterization of the prior distributions has been given so that the resulting Bayes estimator is minimax and/or admissible. When the prior distribution has a hierarchical structure, I have derived conditions under which the hierarchical Bayes estimators are minimax.
2) In the estimation of the component of covariance matrix in a multivariate linear mixed model, I have established a unified theory for the improvement through the truncated method. This problem is related to the estimation of the covariance matrices under the inequality restriction. I have considered several estimation problems under parametric restrictions and have shown the dominance results of Bayesian estimators. Also I have obtained the empirical Bayes estimator of the covariance matrix in the high dimensional cases and shown the theoretical optimality as well as the practical usefulness in data analysis.
3) In the nested error regression model, I have derived the information criterion for selecting explanatory variables. This model is useful in the small area problem, and I have constructed an asymptotically corrected confidence interval of the small area mean and an asymptotically corrected test statistic for the linear hypothesis.
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Report
(5 results)
Research Products
(23 results)
