Abstract
We provide the lacking theory for a test of normality based on a weighted \(L^2\)-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.
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The authors would like to thank two anonymous referees for their careful reading of the manuscript and for helpful suggestions.
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Henze, N., Koch, S. On a test of normality based on the empirical moment generating function. Stat Papers 61, 17–29 (2020). https://doi.org/10.1007/s00362-017-0923-7
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DOI: https://doi.org/10.1007/s00362-017-0923-7
Keywords
- Test of normality
- Empirical moment generating function
- Weighted \(L^2\)-statistic
- Consistency
- Contiguous alternatives