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Some critical remarks on Zhang's gamma test for independence

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  • Klein, Ingo
  • Tinkl, Fabian

Abstract

Zhang (2008) defines the quotient correlation coefficient to test for dependence and tail dependence of bivariate random samples. He shows that asymptotically the test statistics are gamma distributed. Therefore, he called the corresponding test gamma test. We want to investigate the speed of convergence by a simulation study. Zhang discusses a rank-based version of this gamma test that depends on random numbers drawn from a standard Frechet distribution. We propose an alternative that does not depend on random numbers. We compare the size and the power of this alternative with the well-known t-test, the van der Waerden and the Spearman rank test. Zhang proposes his gamma test also for situations where the dependence is neither strictly increasing nor strictly decreasing. In contrast to this, we show that the quotient correlation coefficient can only measure monotone patterns of dependence.

Suggested Citation

  • Klein, Ingo & Tinkl, Fabian, 2011. "Some critical remarks on Zhang's gamma test for independence," Discussion Papers 87/2010, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
  • Handle: RePEc:zbw:faucse:872010
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    1. 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.
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    Keywords

    test on dependence; rank correlation test; Spearman's p; copula; Lehmann ordering;

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