A study of the power and robustness of a new test for independence against contiguous alternatives

Abstract

Various association measures have been proposed in the literature that equal zero when the associated random variables are independent. However many measures, (e.g., Kendall’s tau), may equal zero even in the presence of an association between the random variables. In order to overcome this drawback, Bergsma and Dassios (2014) proposed a modification of Kendall’s tau, (denoted as $\tau^{*}$), which is non-negative and zero if and only if independence holds. In this article, we investigate the robustness properties and the asymptotic distributions of $\tau^{*}$ and some other well-known measures of association under null and contiguous alternatives. Based on these asymptotic distributions under contiguous alternatives, we study the asymptotic power of the test based on $\tau^{*}$ under contiguous alternatives and compare its performance with the performance of other well-known tests available in the literature.