A general approach for testing independence in Hilbert spaces

  • We generalize the projection correlation idea for testing independence of random vectors which is known as a powerful method in multivariate analysis. A universal Hilbert space approach makes the new testing procedures useful in various cases and ensures the applicability to high or even infinite dimensional data. We prove that the new tests keep the significance level under the null hypothesis of independence exactly and can detect any alternative of dependence in the limit, in particular in settings where the dimensions of the observations is infinite or tend to infinity simultaneously with the sample size. Simulations demonstrate that the generalization does not impair the good performance of the approach and confirm our theoretical findings. Furthermore, we describe the implementation of the new approach and present a real data example for illustration.

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Metadaten
Author:Daniel Gaigall, Shunyao Wu, Hua Liang
DOI:https://doi.org/10.1016/j.jmva.2024.105384
ISSN:1095-7243 (online)
ISSN:0047-259X (print)
Parent Title (English):Journal of Multivariate Analysis
Publisher:Elsevier
Place of publication:Amsterdam
Document Type:Article
Language:English
Year of Completion:2024
Date of first Publication:2024/11/16
Tag:High dimensional data; Hilbert space; Independence test; Projection; U-statistic
Volume:206
Article Number:105384
Length:19 Seiten
Note:
Corresponding author: Daniel Gaigall
Peer Review:Ja
Link:https://doi.org/10.1016/j.jmva.2024.105384
Zugriffsart:weltweit
Institutes:FH Aachen / Fachbereich Medizintechnik und Technomathematik
open_access (DINI-Set):open_access
collections:Verlag / Elsevier
Open Access / Hybrid
Geförderte OA-Publikationen / DEAL Elsevier
Licence (German): Creative Commons - Namensnennung