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This paper introduces the \textit{weighted partial copula} function fortesting conditional independence. The proposed test procedure results fromthese two ingredients: (i) the test statistic is an explicit Cramer-von Misestransformation of the \textit{weighted partial copula}, (ii) the regions ofrejection are computed using a bootstrap procedure which mimics conditionalindependence by generating samples from the product measure of the estimatedconditional marginals. Under conditional independence, the weak convergence ofthe \textit{weighted partial copula proces}s is established when the marginalsare estimated using a smoothed local linear estimator. Finally, an experimentalsection demonstrates that the proposed test has competitive power compared torecent state-of-the-art methods such as kernel-based test.

Conditional independence testing via weighted partial copulas and nearest neighbors