mnt - Affine Invariant Tests of Multivariate Normality
Various affine invariant multivariate normality tests are
provided. It is designed to accompany the survey article Ebner,
B. and Henze, N. (2020) <arXiv:2004.07332> titled "Tests for
multivariate normality -- a critical review with emphasis on
weighted L^2-statistics". We implement new and time honoured
L^2-type tests of multivariate normality, such as the
Baringhaus-Henze-Epps-Pulley (BHEP) test, the Henze-Zirkler
test, the test of Henze-Jiménes-Gamero, the test of
Henze-Jiménes-Gamero-Meintanis, the test of Henze-Visage, the
Dörr-Ebner-Henze test based on harmonic oscillator and the
Dörr-Ebner-Henze test based on a double estimation in a PDE.
Secondly, we include the measures of multivariate skewness and
kurtosis by Mardia, Koziol, Malkovich and Afifi and Móri,
Rohatgi and Székely, as well as the associated tests. Thirdly,
we include the tests of multivariate normality by Cox and
Small, the 'energy' test of Székely and Rizzo, the tests based
on spherical harmonics by Manzotti and Quiroz and the test of
Pudelko. All the functions and tests need the data to be a n x
d matrix where n is the samplesize (number of rows) and d is
the dimension (number of columns).
