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

Ebner, Bruno 1; Henze, Norbert 1
1 Institut für Stochastik (STOCH), Karlsruher Institut für Technologie (KIT)


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 contrary 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 the limiting Gaussian process. We solve the associated integral equation and present the corresponding eigenvalues.

Zugehörige Institution(en) am KIT Institut für Stochastik (STOCH)
Publikationstyp Forschungsbericht/Preprint
Publikationsdatum 10.09.2021
Sprache Englisch
Identifikator KITopen-ID: 1000149098
Umfang 11 S.
Nachgewiesen in arXiv
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