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# Normality Testing of High-Dimensional Data Based on Principle Component and Jarque–Bera Statistics

by 1,2 and 1,*
1
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China
2
School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China
*
Author to whom correspondence should be addressed.
Stats 2021, 4(1), 216-227; https://doi.org/10.3390/stats4010016
Received: 28 January 2021 / Revised: 10 March 2021 / Accepted: 12 March 2021 / Published: 17 March 2021
(This article belongs to the Section Computational Statistics)
The testing of high-dimensional normality is an important issue and has been intensively studied in the literature, it depends on the variance–covariance matrix of the sample and numerous methods have been proposed to reduce its complexity. Principle component analysis (PCA) has been widely used in high dimensions, since it can project high-dimensional data into a lower-dimensional orthogonal space. The normality of the reduced data can then be evaluated by Jarque–Bera (JB) statistics in each principle direction. We propose a combined test statistic—the summation of one-way JB statistics upon the independence of the principle directions—to test the multivariate normality of data in high dimensions. The performance of the proposed method is illustrated by the empirical power of the simulated normal and non-normal data. Two real data examples show the validity of our proposed method. View Full-Text
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MDPI and ACS Style

Song, Y.; Zhao, X. Normality Testing of High-Dimensional Data Based on Principle Component and Jarque–Bera Statistics. Stats 2021, 4, 216-227. https://doi.org/10.3390/stats4010016

AMA Style

Song Y, Zhao X. Normality Testing of High-Dimensional Data Based on Principle Component and Jarque–Bera Statistics. Stats. 2021; 4(1):216-227. https://doi.org/10.3390/stats4010016

Chicago/Turabian Style

Song, Yanan; Zhao, Xuejing. 2021. "Normality Testing of High-Dimensional Data Based on Principle Component and Jarque–Bera Statistics" Stats 4, no. 1: 216-227. https://doi.org/10.3390/stats4010016

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