Simpson’s Paradox for Kendall’s Rank Coefficient

Pierre Zuyderhoff, Michel Denuit and Julien Trufin ()
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Pierre Zuyderhoff: University of Nottingham
Michel Denuit: UCLouvain
Julien Trufin: Université Libre de Bruxelles (ULB)

Methodology and Computing in Applied Probability, 2025, vol. 27, issue 2, 1-14

Abstract: Abstract This note revisits Simpson’s paradox and discusses confounding effects of hidden covariates on Kendall’s tau. As a result, observed correlation may vanish or even revert. More specifically, a decomposition of Kendall’s tau in the presence of subgroups is established, a formal definition of Simpson’s paradox for Kendall’s tau is given and some simple examples of paradoxical situations in the insurance domain are provided. Finally, necessary and sufficient conditions for a Simpson’s paradox to occur are studied.

Keywords: Kendall’s tau; Covariates; Simpson’s paradox; 62H20 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11009-025-10161-x

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