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.

本研究涉及高维数据的统计检验问题。首先，我们处理均值向量同质性的检验问题，即检验所有均值向量是否相等。在总体分布服从多元正态的条件下，提出了检验准则。通过模拟研究，我证实当总体分布为多元t时，检验标准的精度是有价值的。我提出了包含多元正态分布的广义总体分布下的其他检验统计量。此外，我们提出了一种测试高维数据多元正态性的测试标准。通过仿真，我们验证了建议的精度随着样本量和维度的增大而变得良好。

项目成果

Testing homogeneity of mean vectors under heteroscedasticity in high-dimension

高维异方差下均值向量同质性检验

• 发表时间: 2013
• 作者: 山田隆行;姫野哲人
• 通讯作者: 姫野哲人

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.;Himeno; T
• 通讯作者: T

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
• 影响因子: 1.6
• 作者: Himeno; T.;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: Takayuki Yamada; Tetsuto Himeno
• 通讯作者: Tetsuto Himeno

Testing homogeneity of mean vectors under heteroscedasticity in high-dimension

高维异方差下均值向量同质性检验

• 作者: 山田隆行; 姫野哲人
• 通讯作者: 姫野哲人