New developments of theories in multivariate statistical inference and their applications

多元统计推断理论新进展及其应用

• 批准号: 21540114
• 负责人: KUBOKAWA Tatsuya
• 金额: $ 2.91万
• 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: 2009
• 资助国家: 日本
• 起止时间: 2009-04-01 至 2014-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21540114/
• 关键词: 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

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.

在本研究项目中，在多元统计模型的估计、假设检验、预测和变量选择方面提出了新的程序，并发展了调整新程序的理论。特别是，我们处理了传统方法有缺陷或不可用的问题、模型或情况，然后我们试图推导并建议可以解决问题的程序。(1)小区域估计的均方误差和可信区间的高阶渐近修正；(2)连续和离散混合模型下小区域估计的基准问题；(3)线性混合模型中的Bartlett校正和变量选择方法；(4)线性判别的高维过程；(5)多维参数估计的最优性。

项目成果

A unified approach to non-minimaxity of sets of linear combinations of restricted location estimators

限制位置估计器线性组合集合非极小极大的统一方法

• 发表时间: 2011
• 期刊: Journed of Multivariate Analysis
• 作者: 久保川達也;W.E.Strawderman
• 通讯作者: W.E.Strawderman

Integral inequality for minimaxity in the Stein problem

斯坦因问题中极小极大的积分不等式

• 发表时间: 2009
• 期刊: Journal of the Japan Statistical Society
• 作者: 板谷雄一;長谷川武光;細田陽介;T. Kubokawa
• 通讯作者: T. Kubokawa

Asymptotic Expansion and Estimation of EPMC for Linear Classification Rules in High Dimension.

高维线性分类规则的EPMC渐近展开和估计。

• 发表时间: 2013
• 期刊: Journal of Multivariate Analysis
• 影响因子: 1.6
• 作者: 久保川達也;兵頭昌;Muni. Srivastava
• 通讯作者: Muni. Srivastava

An empirical Bayes information criterion for selecting variables in linear mixed models

用于在线性混合模型中选择变量的经验贝叶斯信息准则

• 发表时间: 2010
• 期刊: Journal of the Japan Statistical Society
• 作者: T.Hasegawa;Y.Hosoda;K.Hirai;中本敦浩;T. Kubokawa and M.S. Srivastava
• 通讯作者: T. Kubokawa and M.S. Srivastava

Dominance properties of constrained Bayes and empirical Bayes estimators

约束贝叶斯和经验贝叶斯估计量的显性属性

• 发表时间: 2013
• 期刊: Bernoulli
• 影响因子: 1.5
• 作者: Yu.HIGUCHI;A.NAKAMOTO;K.OTA;T.SAKUMA;堀口正之;T. Kubokawa and W.E. Strawderman
• 通讯作者: T. Kubokawa and W.E. Strawderman