English

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

Statistics Theory 2021-09-13 v1 Statistics Theory

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.

Keywords

Cite

@article{arxiv.2109.04897,
  title  = {On the eigenvalues associated with the limit null distribution of the Epps-Pulley test of normality},
  author = {Bruno Ebner and Norbert Henze},
  journal= {arXiv preprint arXiv:2109.04897},
  year   = {2021}
}

Comments

11 pages, 3 Tables