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On testing equality of pairwise rank correlations in a multivariate random vector

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  • Gaißer, Sandra
  • Schmid, Friedrich

Abstract

Spearman's rank-correlation coefficient (also called Spearman's rho) represents one of the best-known measures to quantify the degree of dependence between two random variables. As a copula-based dependence measure, it is invariant with respect to the distribution's univariate marginal distribution functions. In this paper, we consider statistical tests for the hypothesis that all pairwise Spearman's rank correlation coefficients in a multivariate random vector are equal. The tests are nonparametric and their asymptotic distributions are derived based on the asymptotic behavior of the empirical copula process. Only weak assumptions on the distribution function, such as continuity of the marginal distributions and continuous partial differentiability of the copula, are required for obtaining the results. A nonparametric bootstrap method is suggested for either estimating unknown parameters of the test statistics or for determining the associated critical values. We present a simulation study in order to investigate the power of the proposed tests. The results are compared to a classical parametric test for equal pairwise Pearson's correlation coefficients in a multivariate random vector. The general setting also allows the derivation of a test for stochastic independence based on Spearman's rho.

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  • Gaißer, Sandra & Schmid, Friedrich, 2010. "On testing equality of pairwise rank correlations in a multivariate random vector," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2598-2615, November.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:10:p:2598-2615
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    References listed on IDEAS

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    1. Naik, Dayanand N. & Helu, Amal, 2007. "On testing equality of intraclass correlations under unequal family sizes," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6498-6510, August.
    2. Schmid, Friedrich & Schmidt, Rafael, 2007. "Multivariate conditional versions of Spearman's rho and related measures of tail dependence," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1123-1140, July.
    3. Wu, Mi-Xia & Yu, Kai F. & Liu, Aiyi, 2009. "Exact inference on contrasts in means of intraclass correlation models with missing responses," Journal of Multivariate Analysis, Elsevier, vol. 100(2), pages 301-308, February.
    4. 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.
    5. Genest, Christian & Rémillard, Bruno & Beaudoin, David, 2009. "Goodness-of-fit tests for copulas: A review and a power study," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 199-213, April.
    6. Jean-François Quessy, 2009. "Theoretical efficiency comparisons of independence tests based on multivariate versions of Spearman’s rho," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(3), pages 315-338, November.
    7. Helu, Amal & Naik, Dayanand N., 2006. "Estimation of interclass correlation via a Kotz-type distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1523-1534, December.
    8. Cornelia Savu & Mark Trede, 2008. "Goodness-of-fit tests for parametric families of Archimedean copulas," Quantitative Finance, Taylor & Francis Journals, vol. 8(2), pages 109-116.
    9. Seo, Takashi & Kikuchi, Jun & Koizumi, Kazuyuki, 2006. "On simultaneous confidence intervals for all contrasts in the means of the intraclass correlation model with missing data," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 1976-1983, October.
    10. Fermanian, Jean-David, 2005. "Goodness-of-fit tests for copulas," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 119-152, July.
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    1. Wied, Dominik & Dehling, Herold & van Kampen, Maarten & Vogel, Daniel, 2014. "A fluctuation test for constant Spearman’s rho with nuisance-free limit distribution," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 723-736.
    2. García, Jesús E. & González-López, V.A. & Nelsen, R.B., 2013. "A new index to measure positive dependence in trivariate distributions," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 481-495.
    3. Dominik Wied, 2017. "A nonparametric test for a constant correlation matrix," Econometric Reviews, Taylor & Francis Journals, vol. 36(10), pages 1157-1172, November.

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