Tests for multivariate normality—a critical review with emphasis on weighted L2-statistics

• Bruno Ebner ^[1] ; Norbert Henze ^[1]
  1. [1] Institute of Stochastics, Karlsruhe Institute of Technology (KIT), Englerstr. 2, D-76133, Karlsruhe, Germany
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 29, Nº. 4, 2020, págs. 845-892
• Idioma: inglés
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• Resumen

  • 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 L2-statistics. Since weighted L2-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.