A consistent test of independence based on a sign covariance related to Kendall%26apos;s tau

作者：Bergsma Wicher^*; Dassios Angelos

来源：Bernoulli, 2014, 20(2): 1006-1028.

DOI：10.3150/13-BEJ514

• concordance
• copula
• discordance
• measure of association
• ordinal data
• permutation test
• sign test

The most popular ways to test for independence of two ordinal random variables are by means of Kendall%26apos;s tau and Spearman%26apos;s rho. However, such tests are not consistent, only having power for alternatives with %26quot;monotonic%26quot; association. In this paper, we introduce a natural extension of Kendall%26apos;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%26apos;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.

• 出版日期2014-5