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A multivariate rank test of independence based on a multiparametric polynomial copula

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  • Mangold, Benedikt

Abstract

This paper introduces a copula based multivariate rank test for independence extending existing approaches from literature to p dimensions. Then, a multiparametric p-dimensional generalization of the FGM copula is provided that can model the behavior in each vertex of the p-dimensional unit cube using exactly one parameter per vertex - the family of polynomial copulas. The independence copula is nested in this family if and only if every parameter is zero. In this case, a popular way to test for independence is comparing an estimate of the vector of parameters to a vector containing zeros only. Unfortunately, due to the mere quantity of parameters, no established estimation procedure can be used in higher dimensions. Instead, the developed multivariate rank test is applied sequentially to every parameter to test for joint squared deviation from independence. Applying this new test to the polynomial copula results in the new vertex test which is a test for independence with focus on the high dimensional tail regions. It is compared to similar nonparametric rank tests of independence by means of calculation time and power under several alternatives and sample sizes.

Suggested Citation

  • 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.
    • Handle: RePEc:zbw:iwqwdp:102015
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    References listed on IDEAS

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    1. Schmid, Friedrich & Schmidt, Rafael, 2007. "Multivariate extensions of Spearman's rho and related statistics," Statistics & Probability Letters, Elsevier, vol. 77(4), pages 407-416, February.
    2. 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.
    3. Hofert, Marius & Maechler, Martin, 2011. "Nested Archimedean Copulas Meet R: The nacopula Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 39(i09).
    4. Kojadinovic, Ivan & Yan, Jun, 2010. "Modeling Multivariate Distributions with Continuous Margins Using the copula R Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 34(i09).
    5. Christian Genest & Bruno Rémillard, 2004. "Test of independence and randomness based on the empirical copula process," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 335-369, December.
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    Cited by:

    1. Mangold, Benedikt, 2017. "New concepts of symmetry for copulas," FAU Discussion Papers in Economics 06/2017, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics, revised 2017.
    2. Stübinger, Johannes & Mangold, Benedikt & Krauss, Christopher, 2016. "Statistical arbitrage with vine copulas," FAU Discussion Papers in Economics 11/2016, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.

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    Keywords

    rank-based inference; multiparametric; copula; independence; dependogramm; partial dependence; multivariate tail;
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