Tests of independence and randomness for arbitrary data using copula-based covariances

In this article, we study tests of independence for data with arbitrary distributions in the non-serial case, i.e., for independent and identically distributed random vectors, as well as in the serial case, i.e., for time series. These tests are derived from copula-based covariances and their multiv...

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Bibliographic Details
Published inJournal of multivariate analysis Vol. 201; p. 105273
Main Authors Nasri, Bouchra R., Rémillard, Bruno N.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.05.2024
Subjects
Independence
Multilinear copula
Randomness
Savages’s coefficient
Spearman’s rho
Van der Waerden’s coefficient
secondary
Van der Waerden’s coefficient
Savages’s coefficient
Spearman’s rho
Independence
Multilinear copula
Randomness
primary
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Summary:In this article, we study tests of independence for data with arbitrary distributions in the non-serial case, i.e., for independent and identically distributed random vectors, as well as in the serial case, i.e., for time series. These tests are derived from copula-based covariances and their multivariate extensions using Möbius transforms. We find the asymptotic distributions of these statistics under the null hypothesis of independence or randomness, as well as under contiguous alternatives. This enables us to find out locally most powerful test statistics for some alternatives, whatever the margins. Numerical experiments are performed for Wald’s type combinations of these statistics to assess the finite sample performance.
ISSN:0047-259X
1095-7243
DOI:10.1016/j.jmva.2023.105273