Titre

Exact first moments of the RV coefficient by invariant orthogonal integration

Type
article
Institution
UNIL/CHUV/Unisanté + institutions partenaires
Périodique
Auteur(s)
Bavaud, François
Auteure/Auteur
Liens vers les personnes
Liens vers les unités
ISSN
0047-259X
Statut éditorial
Publié
Date de publication
2023-11
Volume
198
Première page
105227
Peer-reviewed
Oui
Langue
anglais
Résumé
The RV coefficient measures the similarity between two multivariate configurations, and its significance testing has attracted various proposals in the last decades. We present a new approach, the invariant orthogonal integration, permitting to obtain the exact first four moments of the RV coefficient under the null hypothesis.
Our proposal can be applied to any multivariate setting endowed with Euclidean distances between the observations. It also covers the weighted setting of observations of unequal importance, where the exchangeability assumption, justifying the usual permutation tests, breaks down.
The proposed RV moments express as simple functions of the kernel eigenvalues occurring in the weighted multidimensional scaling of the two configurations (spectral effective dimensionality, spectral skewness and spectral excess kurtosis). The expressions for the third and fourth moments seem original, and explain the marked asymmetry and kurtosis of the RV coefficient. They permit to test the significance of the RV coefficient by Cornish–Fisher cumulant expansion, beyond the normal approximation, as illustrated on a small dataset.
The first three moments can be obtained by elementary means, but computing the fourth moment requires a more sophisticated apparatus, the Weingarten calculus for orthogonal groups.
Sujets

Invariant orthogonal ...

RV coefficient

Spectral moments

Weighted multidimensi...

Weingarten calculus

PID Serval
serval:BIB_F2DF52BE9BF4
DOI
WOS
Permalien
Open Access
Oui
Date de création
2024-10-04T09:39:46.862Z
Date de création dans IRIS
2025-05-21T05:10:14Z
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Nom

Bavaud_2023_Exact first moments of the RV coefficient by invariant orthogonal integration.pdf

Version du manuscrit

published

Licence

https://creativecommons.org/licenses/by/4.0

Taille

865.07 KB

Format

Adobe PDF

PID Serval

serval:BIB_F2DF52BE9BF4.P001

URN

urn:nbn:ch:serval-BIB_F2DF52BE9BF42

Somme de contrôle

(MD5):9148dde92d7d79feb726c8a85af16875