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New invariant and consistent chi-squared type goodness-of-fit tests for multivariate normality and a related comparative simulation study

Author

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  • Vassilly Voinov
  • Natalie Pya
  • Rashid Makarov
  • Yevgeniy Voinov

Abstract

New invariant and consistent goodness-of-fit tests for multivariate normality are introduced. Tests are based on the Karhunen–Loève transformation of a multidimensional sample from a population. A comparison of simulated powers of tests and other well-known tests with respect to some alternatives is given. The simulation study demonstrates that power of the proposed McCull test almost does not depend on the number of grouping cells. The test shows an advantage over other chi-squared type tests. However, averaged over all of the simulated conditions examined in this article, the Anderson–Darling type and the Cramer–von Mises type tests seem to be the best.

Suggested Citation

  • Vassilly Voinov & Natalie Pya & Rashid Makarov & Yevgeniy Voinov, 2016. "New invariant and consistent chi-squared type goodness-of-fit tests for multivariate normality and a related comparative simulation study," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(11), pages 3249-3263, June.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:11:p:3249-3263
    DOI: 10.1080/03610926.2014.901370
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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. Surya T. Tokdar & Ryan Martin, 2021. "Bayesian Test of Normality Versus a Dirichlet Process Mixture Alternative," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 66-96, May.
    3. Norbert Henze & María Dolores Jiménez‐Gamero, 2021. "A test for Gaussianity in Hilbert spaces via the empirical characteristic functional," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 406-428, June.
    4. 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.
    5. 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.
    6. 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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