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A powerful test for multivariate normality

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  • Ming Zhou
  • Yongzhao Shao

Abstract

This paper investigates a new test for normality that is easy for biomedical researchers to understand and easy to implement in all dimensions. In terms of power comparison against a broad range of alternatives, the new test outperforms the best known competitors in the literature as demonstrated by simulation results. In addition, the proposed test is illustrated using data from real biomedical studies.

Suggested Citation

  • Ming Zhou & Yongzhao Shao, 2014. "A powerful test for multivariate normality," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(2), pages 351-363, February.
    • Handle: RePEc:taf:japsta:v:41:y:2014:i:2:p:351-363
    DOI: 10.1080/02664763.2013.839637
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    References listed on IDEAS

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    1. Jurgen A. Doornik & Henrik Hansen, 2008. "An Omnibus Test for Univariate and Multivariate Normality," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 927-939, December.
    2. L. Baringhaus & N. Henze, 1988. "A consistent test for multivariate normality based on the empirical characteristic function," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 35(1), pages 339-348, December.
    3. N. J. H. Small, 1980. "Marginal Skewness and Kurtosis in Testing Multivariate Normality," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(1), pages 85-87, March.
    4. Coin, Daniele, 2008. "A goodness-of-fit test for normality based on polynomial regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2185-2198, January.
    5. Shao, Yongzhao & Zhou, Ming, 2010. "A characterization of multivariate normality through univariate projections," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2637-2640, November.
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    Cited by:

    1. Wanfang Chen & Marc G. Genton, 2023. "Are You All Normal? It Depends!," International Statistical Review, International Statistical Institute, vol. 91(1), pages 114-139, April.
    2. Francisca Rego & Valentina Sommovigo & Ilaria Setti & Anna Giardini & Elsa Alves & Julliana Morgado & Marina Maffoni, 2022. "How Supportive Ethical Relationships Are Negatively Related to Palliative Care Professionals’ Negative Affectivity and Moral Distress: A Portuguese Sample," IJERPH, MDPI, vol. 19(7), pages 1-17, March.
    3. Edgar Alva & María Urcia & Vanina Vivas, 2023. "Civic Engagement of Future Citizens: An Insight from Peruvian Students’ Attitudes towards Relevant Societal Issues as Predictors of Expected Conventional Political Participation," Child Indicators Research, Springer;The International Society of Child Indicators (ISCI), vol. 16(5), pages 2187-2221, October.
    4. Renee Fry-McKibbin & Cody Yu-Ling Hsiao & Vance L. Martin, 2017. "Joint tests of contagion with applications to financial crises," CAMA Working Papers 2017-23, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    5. Kurita, Eri & Seo, Takashi, 2022. "Multivariate normality test based on kurtosis with two-step monotone missing data," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    6. Jurgita Arnastauskaitė & Tomas Ruzgas & Mindaugas Bražėnas, 2021. "A New Goodness of Fit Test for Multivariate Normality and Comparative Simulation Study," Mathematics, MDPI, vol. 9(23), pages 1-20, November.
    7. Chowdhury, Joydeep & Dutta, Subhajit & Arellano-Valle, Reinaldo B. & Genton, Marc G., 2022. "Sub-dimensional Mardia measures of multivariate skewness and kurtosis," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    8. Bruno Ebner & Norbert Henze, 2020. "Tests for multivariate normality—a critical review with emphasis on weighted $$L^2$$ L 2 -statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 845-892, December.
    9. Norbert Henze & María Dolores Jiménez-Gamero, 2019. "A new class of tests for multinormality with i.i.d. and garch data based on the empirical moment generating function," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 499-521, June.

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