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Local efficiency of a Cramer-von Mises test of independence

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  • Genest, Christian
  • Quessy, Jean-François
  • Rémillard, Bruno

Abstract

Deheuvels proposed a rank test of independence based on a Cramer-von Mises functional of the empirical copula process. Using a general result on the asymptotic distribution of this process under sequences of contiguous alternatives, the local power curve of Deheuvels' test is computed in the bivariate case and compared to that of competing procedures based on linear rank statistics. The Gil-Pelaez inversion formula is used to make additional comparisons in terms of a natural extension of Pitman's measure of asymptotic relative efficiency.

Suggested Citation

  • Genest, Christian & Quessy, Jean-François & Rémillard, Bruno, 2006. "Local efficiency of a Cramer-von Mises test of independence," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 274-294, January.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:1:p:274-294
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    References listed on IDEAS

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    1. Deheuvels, Paul, 1981. "An asymptotic decomposition for multivariate distribution-free tests of independence," Journal of Multivariate Analysis, Elsevier, vol. 11(1), pages 102-113, March.
    2. David Oakes, 2003. "Copula model generated by Dabrowska's association measure," Biometrika, Biometrika Trust, vol. 90(2), pages 478-481, June.
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    Cited by:

    1. Kojadinovic, Ivan & Yan, Jun, 2010. "Nonparametric rank-based tests of bivariate extreme-value dependence," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2234-2249, October.
    2. Daniel Berg & Jean‐François Quessy, 2009. "Local Power Analyses of Goodness‐of‐fit Tests for Copulas," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 389-412, September.
    3. Talbi, Marwa & de Peretti, Christian & Belkacem, Lotfi, 2020. "Dynamics and causality in distribution between spot and future precious metals: A copula approach," Resources Policy, Elsevier, vol. 66(C).
    4. Claudio G. Borroni, 2019. "Mutual association measures," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(4), pages 571-591, December.
    5. Helmut Herwartz & Simone Maxand, 2020. "Nonparametric tests for independence: a review and comparative simulation study with an application to malnutrition data in India," Statistical Papers, Springer, vol. 61(5), pages 2175-2201, October.
    6. Liu, Xiaochun, 2015. "Modeling time-varying skewness via decomposition for out-of-sample forecast," International Journal of Forecasting, Elsevier, vol. 31(2), pages 296-311.
    7. Berghaus, Betina & Segers, Johan, 2018. "Weak convergence of the weighted empirical beta copula process," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 266-281.
    8. C Genest & J G Nešlehová & B Rémillard & O A Murphy, 2019. "Testing for independence in arbitrary distributions," Biometrika, Biometrika Trust, vol. 106(1), pages 47-68.
    9. Wanat, Stanisław & Papież, Monika & Śmiech, Sławomir, 2014. "Causality in distribution between European stock markets and commodity prices: Using independence test based on the empirical copula," MPRA Paper 57706, University Library of Munich, Germany.
    10. Genest, Christian & Nešlehová, Johanna G. & Rémillard, Bruno, 2017. "Asymptotic behavior of the empirical multilinear copula process under broad conditions," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 82-110.
    11. Bianchi, Pascal & Elgui, Kevin & Portier, François, 2023. "Conditional independence testing via weighted partial copulas," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    12. Mangold, Benedikt, 2017. "A multivariate rank test of independence based on a multiparametric polynomial copula," FAU Discussion Papers in Economics 10/2015, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics, revised 2017.
    13. Helmut Herwartz & Alexander Lange & Simone Maxand, 2022. "Data‐driven identification in SVARs—When and how can statistical characteristics be used to unravel causal relationships?," Economic Inquiry, Western Economic Association International, vol. 60(2), pages 668-693, April.
    14. Bagkavos, D. & Patil, P.N., 2017. "A new test of independence for bivariate observations," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 117-133.

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