Tests for multivariate normality -- a critical review with emphasis on weighted $L^2$-statistics
Statistics Theory
2020-04-17 v1 Statistics Theory
Abstract
This article gives a synopsis on new developments in affine invariant tests for multivariate normality in an i.i.d.-setting, with special emphasis on asymptotic properties of several classes of weighted -statistics. Since weighted -statistics typically have limit normal distributions under fixed alternatives to normality, they open ground for a neighborhood of model validation for normality. The paper also reviews several other invariant tests for this problem, notably the energy test, and it presents the results of a large-scale simulation study. All tests under study are implemented in the accompanying R-package mnt.
Cite
@article{arxiv.2004.07332,
title = {Tests for multivariate normality -- a critical review with emphasis on weighted $L^2$-statistics},
author = {Bruno Ebner and Norbert Henze},
journal= {arXiv preprint arXiv:2004.07332},
year = {2020}
}