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

Bruno Ebner; Norbert Henze

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arXiv · 2109.04897

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

Bruno Ebner·Norbert Henze

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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 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.

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Bruno Ebner, Norbert Henze. 2021-09-10. On the eigenvalues associated with the limit null distribution of the Epps-Pulley test of normality. https://arxiv.org/abs/2109.04897

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