A robust permutation test for Kendall's tau

Abstract

The commonly used way to test for independence of two random variables is by means of Kendall's tau. Given a sample from a biviariate distribution, permutation test using its empirical value under independence is known to be exact. However, in the problem for testing the null hypothesis that the samples are uncorrelated, the permutation test can have asymptotic null rejection probability that is far from the nominal level. To deal with this issue, we advocate using appropriately studentized statistic to yield permutation test. We will show that the studentized permutation test is asymptotically consistent in the general setting when two paired variables are uncorrelated but dependent. Simulation studies demonstrate this desired property across a range of distributional assumptions and sample sizes.

Keywords:

• Consistency of test
• measure of association
• permutation test
• rank correlation
• testing independence

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by National Natural Science Foundation of China [grant numbers 12271005, 11901006] and Natural Science Foundation of Anhui Province [grant number 1908085QA06].