Study on multivariate Statistical models and their inference procedures for analysis of high-dimensional data and its applications

高维数据分析的多元统计模型及其推理过程及其应用研究

• 批准号: 21500283
• 负责人: KONNO Yoshihiko
• 金额: $ 2.83万
• 依托单位: Japan Women's University
• 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 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21500283/
• 关键词: ウィシャート行列; 縮小型推定量; トランケートデータ; ウィシャート分布; 等質錐; 多変量解析; 推測理論; Stein問題; 打ち切りデータ; 高次元データ; Wishart分布

The problem of estimating large covariance matrices of multivariate real normal and complex normal distributions is considered when the dimension of the variables is larger than the number of sample size. The Stein-Haff identities and calculus on eigenstructures for singular Wishart matrices are developed for real and complex cases, respectively. By using these techniques, the unbiased risk estimates for certain class of estimators for the population covariance matrices under an invariant quadratic loss functions are obtained for real and complex cases, respectively.

当变量的维度大于样本量时，考虑了多元实正态分布和复正态分布的大协方差阵的估计问题。给出了实和复数情形下奇异Wishart矩阵的Stein-Haff恒等式和特征结构的微积分。利用这些技巧，分别得到了不变二次损失函数下总体协方差阵的一类估计量的无偏风险估计。

项目成果

Shrinkage estimators for large covariance matrices in multivariate normal distribution

多元正态分布中大协方差矩阵的收缩估计

• 发表时间: 2012
• 作者: Konno;Y.
• 通讯作者: Y.

Shrinkage estimators for large covariance matrices in multivariate real and complex normal distributions under an invariant quadratic loss

• DOI: 10.1016/j.jmva.2009.05.002
• 发表时间: 2009-11-01
• 期刊: JOURNAL OF MULTIVARIATE ANALYSIS
• 影响因子: 1.6
• 作者: Konno, Yoshihiko

goodness-fit test for parametric models based on dependently truncated data

基于相关截断数据的参数模型的拟合优度检验

• 发表时间: 2012
• 期刊: Computational Statistics and Data Analysis
• 影响因子: 1.8
• 作者: Emura;T. and Konno;Y.;A
• 通讯作者: A

Estimation of multivariate complex normal covariance under an invariant quadratic loss

不变二次损失下多元复正态协方差的估计

• 期刊: Communication in statistics--Theory and Method (掲載予定)(Accepted)
• 作者: Konno;Y.;Yoshihiko Konno
• 通讯作者: Yoshihiko Konno

Multivariate normal distribution approaches for dependently left-truncated datta

相关左截断数据的多元正态分布方法

• DOI: 10.1007/s00362-010-0321-x
• 发表时间: 2012
• 期刊: Statistical Paper
• 作者: Takeshi Emura;Yoshihiko Konno
• 通讯作者: Yoshihiko Konno