The Impossibility of Testing for Dependence Using Kendall's τ Under Missing Data of Unknown Form

02/24/2022

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by   Oliver R. Cutbill, et al.

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This paper discusses the statistical inference problem associated with testing for dependence between two continuous random variables using Kendall's τ 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 τ, where robustness is with respect to the form of the missingness-generating process, is impossible.