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Generalizing distance covariance to measure and test multivariate mutual dependence via complete and incomplete V-statistics

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  • Jin, Ze
  • Matteson, David S.

Abstract

We propose three new measures of mutual dependence between multiple random vectors. Each measure is zero if and only if the random vectors are mutually independent. The first generalizes distance covariance from pairwise dependence to mutual dependence, while the other two measures are sums of squared distance covariances. The proposed measures share similar properties and asymptotic distributions with distance covariance, and capture non-linear and non-monotone mutual dependence between the random vectors. Inspired by complete and incomplete V-statistics, we define empirical and simplified empirical measures as a trade-off between the complexity and statistical power when testing mutual independence. The implementation of corresponding tests is demonstrated by both simulation results and real data examples.

Suggested Citation

  • Jin, Ze & Matteson, David S., 2018. "Generalizing distance covariance to measure and test multivariate mutual dependence via complete and incomplete V-statistics," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 304-322.
    • Handle: RePEc:eee:jmvana:v:168:y:2018:i:c:p:304-322
    DOI: 10.1016/j.jmva.2018.08.006
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    Cited by:

    1. Christian Gourieroux & Joann Jasiak, 2023. "Generalized Covariance Estimator," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(4), pages 1315-1327, October.
    2. Beaulieu Guillaume Boglioni & de Micheaux Pierre Lafaye & Ouimet Frédéric, 2021. "Counterexamples to the classical central limit theorem for triplewise independent random variables having a common arbitrary margin," Dependence Modeling, De Gruyter, vol. 9(1), pages 424-438, January.
    3. Krzyśko Mirosław & Smaga Łukasz, 2020. "Measuring and Testing Mutual Dependence of Multivariate Functional Data," Statistics in Transition New Series, Statistics Poland, vol. 21(3), pages 21-37, September.
    4. Mirosław Krzyśko & Łukasz Smaga, 2020. "Measuring and Testing Mutual Dependence of Multivariate Functional Data," Statistics in Transition New Series, Polish Statistical Association, vol. 21(3), pages 21-37, September.

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