Conditional independence testing via weighted partial copulas and nearest neighbors

This paper introduces the $\mathit{\text{weighted}}\mathit{\text{partial}}\mathit{\text{copula}}$ 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 $\mathit{\text{weighted}}\mathit{\text{partial}}\mathit{\text{copula}}$, (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 $\mathit{\text{weighted}}\mathit{\text{partial}}\mathit{\text{copula}}\mathit{\text{proces}}$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.