The Impossibility of Testing for Dependence Using Kendall's $\tau$ Under Missing Data of Unknown Form

Abstract

This paper discusses the statistical inference problem associated with testing for dependence between two continuous random variables using Kendall's $\tau$ in the context of the missing data problem. We prove the worst-case identified set for this measure of association always includes zero. The consequence of this result is that robust inference for dependence using Kendall's $\tau$, where robustness is with respect to the form of the missingness-generating process, is impossible.