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A Comparative Study of Goodness-of-Fit Tests for Multivariate Normality

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  • Romeu, J. L.
  • Ozturk, A.

Abstract

A Monte Carlo power study of 10 multivariate normality goodness-of-fit tests is presented. First, multivariate goodness-of-fit methods and non-normal alternatives are classified according to their characteristics. Then, a measurement tool is defined, validated, and used to assess the performance of the methods, which are then ranked by type of alternative they best detect. Finally, Monte Carlo-derived empirical critical values for the 8 procedures, valid when samples are too small to invoke asymptotic theory, are provided.

Suggested Citation

  • Romeu, J. L. & Ozturk, A., 1993. "A Comparative Study of Goodness-of-Fit Tests for Multivariate Normality," Journal of Multivariate Analysis, Elsevier, vol. 46(2), pages 309-334, August.
    • Handle: RePEc:eee:jmvana:v:46:y:1993:i:2:p:309-334
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    Cited by:

    1. Makigusa, Natsumi & Naito, Kanta, 2020. "Asymptotics and practical aspects of testing normality with kernel methods," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    2. Huffer, Fred W. & Park, Cheolyong, 2007. "A test for elliptical symmetry," Journal of Multivariate Analysis, Elsevier, vol. 98(2), pages 256-281, February.
    3. 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.
    4. Annaliisa Kankainen & Sara Taskinen & Hannu Oja, 2007. "Tests of multinormality based on location vectors and scatter matrices," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 16(3), pages 357-379, November.
    5. Tenreiro, Carlos, 2009. "On the choice of the smoothing parameter for the BHEP goodness-of-fit test," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1038-1053, February.
    6. Tenreiro, Carlos, 2011. "An affine invariant multiple test procedure for assessing multivariate normality," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 1980-1992, May.
    7. Henze, Norbert & Wagner, Thorsten, 1997. "A New Approach to the BHEP Tests for Multivariate Normality," Journal of Multivariate Analysis, Elsevier, vol. 62(1), pages 1-23, July.
    8. 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.
    9. Kim, Namhyun, 2016. "A robustified Jarque–Bera test for multivariate normality," Economics Letters, Elsevier, vol. 140(C), pages 48-52.
    10. Sigut, J. & Pineiro, J. & Moreno, L. & Estevez, J. & Aguilar, R. & Marichal, R., 2005. "A large deviation approach to normality testing," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 741-756, June.
    11. Naito, Kanta, 1998. "Approximation of the Power of Kurtosis Test for Multinormality," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 166-180, May.
    12. Norbert Henze, 2002. "Invariant tests for multivariate normality: a critical review," Statistical Papers, Springer, vol. 43(4), pages 467-506, October.
    13. Beirlant, J. & Mason, D. M. & Vynckier, C., 1999. "Goodness-of-fit analysis for multivariate normality based on generalized quantiles," Computational Statistics & Data Analysis, Elsevier, vol. 30(2), pages 119-142, April.
    14. Yang, Zhen-Hai & Fang, Kai-Tai & Liang, Jia-Juan, 1996. "A characterization of multivariate normal distribution and its application," Statistics & Probability Letters, Elsevier, vol. 30(4), pages 347-352, November.
    15. Kirt Butler & Katsushi Okada, 2009. "The relative contribution of conditional mean and volatility in bivariate returns to international stock market indices," Applied Financial Economics, Taylor & Francis Journals, vol. 19(1), pages 1-15.
    16. Fred Huffer & Cheolyong Park, 2000. "A test for multivariate structure," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(5), pages 633-650.
    17. M. J. Baxter & N. H. Gale, 1998. "Testing for multivariate normality via univariate tests: A case study using lead isotope ratio data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 25(5), pages 671-683, June.
    18. Alessandro Manzotti & Adolfo Quiroz, 2001. "Spherical harmonics in quadratic forms for testing multivariate normality," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(1), pages 87-104, June.
    19. Tan, Ming & Fang, Hong-Bin & Tian, Guo-Liang & Wei, Gang, 2005. "Testing multivariate normality in incomplete data of small sample size," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 164-179, March.
    20. Sirao Wang & Jiajuan Liang & Min Zhou & Huajun Ye, 2022. "Testing Multivariate Normality Based on F -Representative Points," Mathematics, MDPI, vol. 10(22), pages 1-22, November.
    21. Henze, Norbert, 1997. "Extreme smoothing and testing for multivariate normality," Statistics & Probability Letters, Elsevier, vol. 35(3), pages 203-213, October.
    22. Szekely, Gábor J. & Rizzo, Maria L., 2005. "A new test for multivariate normality," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 58-80, March.

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