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Testing high-dimensional normality based on classical skewness and Kurtosis with a possible small sample size

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  • Jiajuan Liang
  • Man-Lai Tang
  • Xuejing Zhao

Abstract

By using the idea of principal component analysis, we propose an approach to applying the classical skewness and kurtosis statistics for detecting univariate normality to testing high-dimensional normality. High-dimensional sample data are projected to the principal component directions on which the classical skewness and kurtosis statistics can be constructed. The theory of spherical distributions is employed to derive the null distributions of the combined statistics constructed from the principal component directions. A Monte Carlo study is carried out to demonstrate the performance of the statistics on controlling type I error rates and a simple power comparison with some existing statistics. The effectiveness of the proposed statistics is illustrated by two real-data examples.

Suggested Citation

  • Jiajuan Liang & Man-Lai Tang & Xuejing Zhao, 2019. "Testing high-dimensional normality based on classical skewness and Kurtosis with a possible small sample size," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(23), pages 5719-5732, December.
    • Handle: RePEc:taf:lstaxx:v:48:y:2019:i:23:p:5719-5732
    DOI: 10.1080/03610926.2018.1520882
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    Cited by:

    1. Zhenzhen Liu & Hang Wang & Ning Li & Jun Zhu & Ziwu Pan & Fen Qin, 2020. "Spatial and Temporal Characteristics and Driving Forces of Vegetation Changes in the Huaihe River Basin from 2003 to 2018," Sustainability, MDPI, vol. 12(6), pages 1-18, March.
    2. Yanan Song & Xuejing Zhao, 2021. "Normality Testing of High-Dimensional Data Based on Principle Component and Jarque–Bera Statistics," Stats, MDPI, vol. 4(1), pages 1-12, March.

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