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

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