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May 2014 A consistent test of independence based on a sign covariance related to Kendall’s tau
Wicher Bergsma, Angelos Dassios
Bernoulli 20(2): 1006-1028 (May 2014). DOI: 10.3150/13-BEJ514

Abstract

The most popular ways to test for independence of two ordinal random variables are by means of Kendall’s tau and Spearman’s rho. However, such tests are not consistent, only having power for alternatives with “monotonic” association. In this paper, we introduce a natural extension of Kendall’s tau, called $\tau^{*}$, which is non-negative and zero if and only if independence holds, thus leading to a consistent independence test. Furthermore, normalization gives a rank correlation which can be used as a measure of dependence, taking values between zero and one. A comparison with alternative measures of dependence for ordinal random variables is given, and it is shown that, in a well-defined sense, $\tau^{*}$ is the simplest, similarly to Kendall’s tau being the simplest of ordinal measures of monotone association. Simulation studies show our test compares well with the alternatives in terms of average $p$-values.

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Wicher Bergsma. Angelos Dassios. "A consistent test of independence based on a sign covariance related to Kendall’s tau." Bernoulli 20 (2) 1006 - 1028, May 2014. https://doi.org/10.3150/13-BEJ514

Information

Published: May 2014
First available in Project Euclid: 28 February 2014

zbMATH: 06291830
MathSciNet: MR3178526
Digital Object Identifier: 10.3150/13-BEJ514

Rights: Copyright © 2014 Bernoulli Society for Mathematical Statistics and Probability

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Vol.20 • No. 2 • May 2014
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