mnt-package: mnt: Affine Invariant Tests of Multivariate Normality
In mnt: Affine Invariant Tests of Multivariate Normality
mnt-package R Documentation
mnt: Affine Invariant Tests of Multivariate Normality
Description
Various affine invariant multivariate normality tests are provided. It is designed to accompany the survey article Ebner, B. and Henze, N. (2020) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s11749-020-00740-0")} 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).
Use with model residuals
The tests implemented in mnt are calibrated for independent
and identically distributed observations. Applying them to residuals
from fitted models requires additional justification, because parameter
estimation may change the null distribution and invalidate the usual
critical values. As discussed by Jimenez-Gamero (2020) and acknowledged
by Ebner and Henze (2020), validity depends on both the test and the
underlying model.
Author(s)
Maintainer: Bruno Ebner bruno.ebner@kit.edu
Authors:
Bruno Ebner bruno.ebner@kit.edu
Lucas Butsch lucas.butsch@gmail.com
Other contributors:
Jaco Visagie jaco.visagie@nwu.ac.za [contributor]
Johann Siemens johann-siemens@web.de [contributor]
References
Jimenez-Gamero, M. D. (2020).
Comments on: Tests for multivariate normality—a critical review
with emphasis on weighted L2-statistics.
TEST, 29, 893–897.
\Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s11749-020-00742-y")}.
Ebner, B. and Henze, N. (2020).
Rejoinder on: Tests for multivariate normality—a critical review
with emphasis on weighted L2-statistics.
TEST, 29, 911–913.
\Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s11749-020-00744-w")}.
mnt documentation built on Sept. 25, 2026, 5:08 p.m.
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| mnt-package | R Documentation |
mnt: Affine Invariant Tests of Multivariate Normality
Description
Various affine invariant multivariate normality tests are provided. It is designed to accompany the survey article Ebner, B. and Henze, N. (2020) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s11749-020-00740-0")} 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).
Use with model residuals
The tests implemented in mnt are calibrated for independent
and identically distributed observations. Applying them to residuals
from fitted models requires additional justification, because parameter
estimation may change the null distribution and invalidate the usual
critical values. As discussed by Jimenez-Gamero (2020) and acknowledged
by Ebner and Henze (2020), validity depends on both the test and the
underlying model.
Author(s)
Maintainer: Bruno Ebner bruno.ebner@kit.edu
Authors:
Bruno Ebner bruno.ebner@kit.edu
Lucas Butsch lucas.butsch@gmail.com
Other contributors:
Jaco Visagie jaco.visagie@nwu.ac.za [contributor]
Johann Siemens johann-siemens@web.de [contributor]
References
Jimenez-Gamero, M. D. (2020). Comments on: Tests for multivariate normality—a critical review with emphasis on weighted L2-statistics. TEST, 29, 893–897. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s11749-020-00742-y")}.
Ebner, B. and Henze, N. (2020). Rejoinder on: Tests for multivariate normality—a critical review with emphasis on weighted L2-statistics. TEST, 29, 911–913. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s11749-020-00744-w")}.
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