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

TL;DR

This paper proves that testing for dependence with Kendall's τ is fundamentally impossible under unknown missing data mechanisms, as the worst-case scenario always includes no dependence.

Contribution

It establishes the impossibility of robust dependence testing with Kendall's τ when the missing data process is unknown, highlighting fundamental limitations.

Findings

Worst-case identified set always includes zero

Robust inference for dependence is impossible under unknown missingness

Kendall's τ cannot reliably test dependence with 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.