A study of robustness for testing problem under non-normality for high-dimensional data

高维数据非正态性下检验问题的鲁棒性研究

• 批准号: 23740085
• 负责人: YAMADA Takayuki
• 金额: $ 1.58万
• 依托单位: Nihon University (2013)The Institute of Statistical Mathematics (2011-2012)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23740085/
• 关键词: 多変量解析; 統計的推測論; 高次元データ; 統計数学; 統計的推測; 国際情報交換; 国際情報交流

This study is concerned with the statistical testing problem for high-dimensional data. Firstly, we dealt with the problem for testing homogeneity of mean vectors, that is, testing that all mean vectors are equal. Under the condition that the population distribution is multivariate normal, testing criterion was being proposed. Through the simulation study, I confirmed that the precision of the testing criterion gets worth when the population distribution is multivariate t. I proposed other testing statistic under a generalized population distribution which contains multivariate normal. In addition, we proposed a testing criterion for testing multivariate normality for high-dimensional data. Through simulation, we validate that the precisions of the proposals become well as the sample size and the dimension are large.

本文研究高维数据的统计检验问题。首先讨论了均值向量的齐性检验问题，即均值向量是否相等的检验问题。在总体服从多元正态分布的条件下，给出了检验准则。通过模拟研究，证实了当总体分布为多元t时，检验准则的精度是值得的。在含有多元正态分布的广义总体分布下，提出了另一种检验统计量。此外，我们还提出了一个检验高维数据多元正态性的检验准则。通过仿真实验，验证了当样本量和维数较大时，所提方法的精度较高。

项目成果

Estimations for some functions of covariance matrix in high dimension under non-normality and its applications

非正态性下高维协方差矩阵某些函数的估计及其应用

• DOI: 10.1016/j.jmva.2014.04.020
• 发表时间: 2014
• 期刊: Journal of Multivariate Analysis
• 影响因子: 1.6
• 作者: Himeno;T. and Yamada;T
• 通讯作者: T

Test for assessing multivariate normality available for high-dimensional data

用于评估高维数据的多元正态性的测试

• 发表时间: 2013
• 作者: Yamada;T. and Himeno;T
• 通讯作者: T

Testing homogeneity of mean vectors under heteroscedasticity in high-dimension

• DOI: 10.1016/j.jmva.2015.02.005
• 发表时间: 2015-07
• 期刊: J. Multivar. Anal.
• 作者: Takayuki Yamada;Tetsuto Himeno

Test for mean vector in high-dimension under non-normality

非正态性下高维均值向量检验

• 发表时间: 2012
• 作者: M.Yadome;Y.Nishiura;T. Teramoto;塩沢裕一;Atsushi Takeuchi;Takayuki Yamada and Tetsuto Himeno
• 通讯作者: Takayuki Yamada and Tetsuto Himeno

Estimations for some functions of covariance matrix in high dimension under non-normality and its application

非正态性下高维协方差矩阵某些函数的估计及其应用

• 作者: Himeno;T. and Yamada T
• 通讯作者: T. and Yamada T