Testing Multivariate Normality Based on Beta-Representative Points

Yiwen Cao, Jiajuan Liang (), Longhao Xu and Jiangrui Kang
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Yiwen Cao: Department of Statistics and Data Science, BNU-HKBU United International College, Zhuhai 519087, China
Jiajuan Liang: Department of Statistics and Data Science, BNU-HKBU United International College, Zhuhai 519087, China
Longhao Xu: Department of Medical Statistics, University Medical Center Göettingen, 37075 Göettingen, Germany
Jiangrui Kang: Department of Statistics and Data Science, BNU-HKBU United International College, Zhuhai 519087, China

Mathematics, 2024, vol. 12, issue 11, 1-16

Abstract: Testing multivariate normality in high-dimensional data analysis has been a long-lasting topic in the area of goodness of fit. Numerous methods for this purpose can be found in the literature. Reviews on different methods given by influential researchers show that new methods keep emerging in the literature from different perspectives. The theory of statistical representative points provides a new perspective to construct tests for multivariate normality. To avoid the difficulty and huge computational load in finding the statistical representative points from a high-dimensional probability distribution, we develop an approach to constructing a test for high-dimensional normal distribution based on the representative points of the simple univariate beta distribution. The representative-points-based approach is extended to the the case that the sample size may be smaller than the dimension. A Monte Carlo study shows that the new test is able to control type I error rates fairly well for both large and small sample sizes when faced with a high dimension. The power of the new test against some non-normal distributions is generally or substantially improved for a set of selected alternative distributions. A real-data example is given for a simple application illustration.

Keywords: affine invariance; beta distribution; chi-square test; multivariate normality; representative points (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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