Limiting behavior of the ICF test for normality under Gram-Charlier alternatives

T. W. Epps

Statistics & Probability Letters, 1999, vol. 42, issue 2, 175-184

Abstract: The integrated characteristic function (ICF) test, introduced by Epps and Pulley (1983, Biometrika 70, 723-726) and Baringhaus and Henze (1988, Metrika 35, 339-348), has become recognized as a powerful omnibus test for univariate and multivariate normality. Although the test statistic is of simple closed form, it is derived as a weighted integral of the squared modulus of the difference between the c.f.s of the standardized sample and the spherical normal. The canonical weight function depends on an arbitrary smoothing parameter that the user must specify. We derive here an approximate lower bound for the power of the ICF test when the data are from a distribution represented as a finite Gram-Charlier expansion. The result sheds light on how the test's power depends on the smoothing parameter and the characteristics of the data.

Keywords: Empirical; characteristic; function; Goodness-of-fit; test; Multivariate; normality (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (10)

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