Simultaneous testing of mean vector and covariance matrix for high-dimensional data

2017 ◽  
Vol 188 ◽  
pp. 82-93 ◽  
Author(s):  
Zhongying Liu ◽  
Baisen Liu ◽  
Shurong Zheng ◽  
Ning-Zhong Shi
Keyword(s):  
Covariance Matrix ◽  
High Dimensional Data ◽  
High Dimensional ◽  
Simultaneous Testing ◽  
Mean Vector

scholarly journals A new test for sphericity of the covariance matrix for high dimensional data

2010 ◽  
Vol 101 (10) ◽  
pp. 2554-2570 ◽  
Author(s):  
Thomas J. Fisher ◽  
Xiaoqian Sun ◽  
Colin M. Gallagher
Keyword(s):  
Covariance Matrix ◽  
High Dimensional Data ◽  
High Dimensional

scholarly journals Normality Testing of High-Dimensional Data Based on Principle Component and Jarque-Bera Statistics

2021 ◽  
Author(s):  
Ya-nan Song ◽  
Xuejing Zhao
Keyword(s):  
Covariance Matrix ◽  
High Dimensional Data ◽  
Simulated Data ◽  
High Dimensional ◽  
Empirical Power ◽  
High Dimensions ◽  
Principle Component ◽  
Orthogonal Space ◽  
Reduced Data ◽  
Variance Covariance Matrix

The testing of high-dimensional normality has been an important issue and has been intensively studied in literatures, it depends on the Variance-Covariance matrix of the sample, numerous methods have been proposed to reduce the complex of the Variance-Covariance matrix. The principle component analysis(PCA) was widely used since it can project the high-dimensional data into lower dimensional orthogonal space, and the normality of the reduced data can be evaluated by Jarque-Bera(JB) statistic on each principle direction. We propose two combined statistics, the summation and the maximum of one-way JB statistics, upon the independency of each principle direction, to test the multivariate normality of data in high dimensions. The performance of the proposed methods is illustrated by the empirical power of the simulated data of normal data and non-normal data. Two real examples show the validity of our proposed methods.

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