# Tests for multivariate normality—a critical review with emphasis on weighted $L^2$-statistics

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

##### 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 L$^{2}$-statistics. Since weighted L$^{2}$-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.

 Zugehörige Institution(en) am KIT Institut für Stochastik (STOCH) Publikationstyp Zeitschriftenaufsatz Publikationsmonat/-jahr 12.2020 Sprache Englisch Identifikator ISSN: 1133-0686, 1863-8260 KITopen-ID: 1000129679 Erschienen in TEST Verlag Springer Band 29 Heft 4 Seiten 845–892 Vorab online veröffentlicht am 01.12.2020 Nachgewiesen in DimensionsWeb of Science
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