Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

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

Version 1 : Received: 23 February 2021 / Approved: 24 February 2021 / Online: 24 February 2021 (11:22:22 CET)
Version 2 : Received: 24 February 2021 / Approved: 25 February 2021 / Online: 25 February 2021 (08:07:12 CET)

A peer-reviewed article of this Preprint also exists.

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

Journal reference: Stats 2021, 4, 16
DOI: 10.3390/stats4010016

Abstract

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.

Subject Areas

Principal component; Jarque-Bera statistic; Normality testing; Empirical power; Simulation

Comments (1)

Comment 1
Received: 25 February 2021
Commenter: Xuejing Zhao
Commenter's Conflict of Interests: Author
Comment: The figures have been verified
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