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Title:Some critical remarks on Zhang's gamma test for independence PDF Logo
Authors:Klein, Ingo
Tinkl, Fabian
Issue Date:2011
Series/Report no.:Diskussionspapiere // Friedrich-Alexander-Universität Erlangen-Nürnberg, Lehrstuhl für Statistik und Ökonometrie 87/2010
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.
Subjects:test on dependence
rank correlation test
Spearman's p
copula
Lehmann ordering
Document Type:Working Paper
Appears in Collections:Diskussionspapiere des Lehrstuhls für Statistik und Ökonometrie, FAU Erlangen-Nürnberg

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