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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. Dominik Wied, 2017. "A nonparametric test for a constant correlation matrix," Econometric Reviews, Taylor & Francis Journals, vol. 36(10), pages 1157-1172, November.
    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. 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.

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