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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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    1. Shalit, Haim, 2012. "Using OLS to test for normality," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 2050-2058.
    2. Wangli Xu & Yanwen Li & Dawo Song, 2013. "Testing normality in mixed models using a transformation method," Statistical Papers, Springer, vol. 54(1), pages 71-84, February.
    3. Schick, Anton & Wang, Yishi & Wefelmeyer, Wolfgang, 2011. "Tests for normality based on density estimators of convolutions," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 337-343, February.
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    5. Kundu, Subrata & Majumdar, Suman & Mukherjee, Kanchan, 2000. "Central Limit Theorems revisited," Statistics & Probability Letters, Elsevier, vol. 47(3), pages 265-275, April.
    6. Norbert Henze, 2002. "Invariant tests for multivariate normality: a critical review," Statistical Papers, Springer, vol. 43(4), pages 467-506, October.
    7. Aldo Goia & Ernesto Salinelli & Pascal Sarda, 2015. "A new powerful version of the BUS test of normality," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(3), pages 449-474, September.
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