  This paper introduces the \textit{weighted partial copula} function for
testing conditional independence. The proposed test procedure results from
these two ingredients: (i) the test statistic is an explicit Cramer-von Mises
transformation of the \textit{weighted partial copula}, (ii) the regions of
rejection are computed using a bootstrap procedure which mimics conditional
independence by generating samples from the product measure of the estimated
conditional marginals. Under conditional independence, the weak convergence of
the \textit{weighted partial copula proces}s is established when the marginals
are estimated using a smoothed local linear estimator. Finally, an experimental
section demonstrates that the proposed test has competitive power compared to
recent state-of-the-art methods such as kernel-based test.
