Testing Multivariate Normality Based on F -Representative Points

Sirao Wang, Jiajuan Liang, Min Zhou and Huajun Ye ()
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Sirao Wang: Faculty of Science and Technology, BNU-HKBU United International College, Zhuhai 519087, China
Jiajuan Liang: Faculty of Science and Technology, BNU-HKBU United International College, Zhuhai 519087, China
Min Zhou: Faculty of Science and Technology, BNU-HKBU United International College, Zhuhai 519087, China
Huajun Ye: Faculty of Science and Technology, BNU-HKBU United International College, Zhuhai 519087, China

Mathematics, 2022, vol. 10, issue 22, 1-22

Abstract: The multivariate normal is a common assumption in many statistical models and methodologies for high-dimensional data analysis. The exploration of approaches to testing multivariate normality never stops. Due to the characteristics of the multivariate normal distribution, most approaches to testing multivariate normality show more or less advantages in their power performance. These approaches can be classified into two types: multivariate and univariate. Using the multivariate normal characteristic by the Mahalanobis distance, we propose an approach to testing multivariate normality based on representative points of the simple univariate F -distribution and the traditional chi-square statistic. This approach provides a new way of improving the traditional chi-square test for goodness-of-fit. A limited Monte Carlo study shows a considerable power improvement of the representative-point-based chi-square test over the traditional one. An illustration of testing goodness-of-fit for three well-known datasets gives consistent results with those from classical methods.

Keywords: affine invariance; chi-squared test; F-distribution; multivariate normality; representative points (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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