Research on derivations of Bayes estimators with decision-theoretical optimality and their applications

决策理论最优性贝叶斯估计量的推导及其应用研究

• 批准号: 16500172
• 负责人: KUBOKAWA Tatsuya
• 金额: $ 2.41万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-16500172/
• 关键词: 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

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.

贝叶斯程序的实用性最近从实际方面得到了认可。在该研究项目中，我从几个统计问题的决策理论观点以及应用程序中的实用性中展示了贝叶斯程序的最佳性。详细信息如下：1）在估计多元正态分布的平均向量时，已经给出了先前分布的表征，以使所得的贝叶斯估计量是最小值和/或可接受的。当先前的分布具有层次结构时，我具有得出的条件，在该条件下，在多变量线性混合模型中，在对协方差矩阵的估计中，我已经建立了一个通过改进的理论，以通过改进的理论，以改善协方差矩阵。截断方法。此问题与在不平等限制下对协方差矩阵的估计有关。我考虑了参数限制下的几个估计问题，并显示了贝叶斯估计器的优势结果。另外，我在高维情况下获得了协方差矩阵的经验贝叶斯估计器，并显示了理论最优性以及数据分析中的实际实用性。3）在嵌套的误差回归模型中，我得出了选择解释性的信息标准变量。该模型在小面积问题中很有用，我已经构建了小面积均值的渐近校正置信区间，并为线性假设构建了渐近校正的测试统计量。

项目成果

線形混合モデルと小地域の推定

线性混合模型和小区域估计

• 发表时间: 2007
• 期刊: 応用統計学 掲載決定(印刷中)
• 作者: Komori;M.;Yamamoto;Y.;Nagaoka;C.;久保川達也
• 通讯作者: 久保川達也

モデル選択-予測・検定・推定の交差点-

模型选择——预测、测试和估计的交叉点——

• 发表时间: 2004
• 作者: 下平英寿;伊藤秀一;久保川達也;竹内啓
• 通讯作者: 竹内啓

Estimation in a linear regression model under the Kullback-Leibler loss and its application to model selection

Kullback-Leibler 损失下线性回归模型的估计及其在模型选择中的应用

• 发表时间: 2007
• 期刊: J.Statistical Planning and Inference 137
• 作者: Mostafa Al Masum Shaikh;Helmut Prendinger;Mitsuru Ishizuka;和泉 諭;T.Kubokawa and H.Tsukuma
• 通讯作者: T.Kubokawa and H.Tsukuma

Linear Mixed Model and Small Area Estimation

线性混合模型和小面积估计

• 发表时间: 2007
• 作者: T.Kubokawa;M.S.Srivastava;T.Kubokawa;久保川 達也;T. Kubokawa
• 通讯作者: T. Kubokawa

Minimax multivariate empirical Bayes estimators under multicollinearlity

多重共线性下的极小极大多元经验贝叶斯估计

• 发表时间: 2005
• 期刊: Journal of Multivariate Analysis 93
• 作者: T.Kubokawa;M.-T.Tsai(共著);久保川 達也;M.S. Srivastava(共著);M. S. Srivastava and T. Kubokawa
• 通讯作者: M. S. Srivastava and T. Kubokawa