On the eigenvalues associated with the limit null distribution of the Epps-Pulley test of normality

Bruno Ebner () and Norbert Henze ()
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Bruno Ebner: Karlsruhe Institute of Technology (KIT)
Norbert Henze: Karlsruhe Institute of Technology (KIT)

Statistical Papers, 2023, vol. 64, issue 3, No 1, 739-752

Abstract: Abstract The Shapiro–Wilk test (SW) and the Anderson–Darling test (AD) turned out to be strong procedures for testing for normality. They are joined by a class of tests for normality proposed by Epps and Pulley that, in contrast to SW and AD, have been extended by Baringhaus and Henze to yield easy-to-use affine invariant and universally consistent tests for normality in any dimension. The limit null distribution of the Epps–Pulley test involves a sequences of eigenvalues of a certain integral operator induced by the covariance kernel of a Gaussian process. We solve the associated integral equation and present the corresponding eigenvalues.

Keywords: Test for normality; Integral operator; Fredholm determinant; Primary 62F03; Secondary 65C60; 65R20 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00362-022-01336-6

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