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

Bruno Ebner () and Norbert Henze ()
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Bruno Ebner: Karlsruhe Institute of Technology (KIT)
Norbert Henze: Karlsruhe Institute of Technology (KIT)

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2020, vol. 29, issue 4, No 1, 845-892

Abstract: 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 $$L^2$$ L 2 -statistics. Since weighted $$L^2$$ 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.

Keywords: Test for multivariate normality; Weighted $$L^2$$ L 2 -statistic; Affine invariance; Consistency; 62H1510; 62G20 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (10)

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DOI: 10.1007/s11749-020-00740-0

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