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On a test of normality based on the empirical moment generating function

Author

Listed:
  • Norbert Henze

    (Karlsruhe Institute of Technology (KIT))

  • Stefan Koch

    (University of Mannheim, A5 6)

Abstract

We provide the lacking theory for a test of normality based on a weighted $$L^2$$L2-statistic that employs the empirical moment generating function. The test statistic has a non-degenerate asymptotic null distribution, and the test is consistent against general alternatives. As a parameter associated with the weight function tends to infinity, an affine transformation of the test statistic approaches squared sample skewness.

Suggested Citation

  • Norbert Henze & Stefan Koch, 2020. "On a test of normality based on the empirical moment generating function," Statistical Papers, Springer, vol. 61(1), pages 17-29, February.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:1:d:10.1007_s00362-017-0923-7
    DOI: 10.1007/s00362-017-0923-7
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    References listed on IDEAS

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    6. Norbert Henze, 2002. "Invariant tests for multivariate normality: a critical review," Statistical Papers, Springer, vol. 43(4), pages 467-506, October.
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