Abstract:In this paper, we revisit the notion of partial copula, originally introduced to test conditional independence, highlighting its capability to represent the dependence between two random variables after removing their dependence with a covariate. Building upon results previously presented in the literature, we show that partial copulas can be seen as a nonlinear analogue of partial correlation. Then, we prove several results showing how dependence properties of the conditional copulas constrain the form of the partial copula. Finally, a simulation study is conducted to illustrate the results and to show the potential of the partial copula as a way to describe covariate-adjusted statistical dependence. This highlights the potential of the method to be used in causal inference problems and to recover the true sign of a causal effect.
| Subjects: | Methodology (stat.ME) |
| Cite as: | arXiv:2603.10941 [stat.ME] |
| (or arXiv:2603.10941v2 [stat.ME] for this version) | |
| https://doi.org/10.48550/arXiv.2603.10941 arXiv-issued DOI via DataCite |
From: Vinícius Litvinoff Justus [view email]
[v1]
Wed, 11 Mar 2026 16:28:00 UTC (31,121 KB)
[v2]
Sun, 24 May 2026 17:00:38 UTC (2,568 KB)
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