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

Yanan Song and Xuejing Zhao
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Yanan Song: School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China
Xuejing Zhao: School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China

Stats, 2021, vol. 4, issue 1, 1-12

Abstract: 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.

Keywords: principal component; Jarque–Bera statistic; normality testing; empirical power; simulation (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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