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

Norbert Henze () and Stefan Koch ()
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Norbert Henze: Karlsruhe Institute of Technology (KIT)
Stefan Koch: University of Mannheim, A5 6

Statistical Papers, 2020, vol. 61, issue 1, No 2, 17-29

Abstract: 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.

Keywords: Test of normality; Empirical moment generating function; Weighted $$L^2$$ L 2 -statistic; Consistency; Contiguous alternatives; 62F05; 62G10 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00362-017-0923-7

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