Conditional independence testing via weighted partial copulas

The test statistic proposed in this paper is an explicit Cramér–von Mises transformation of a certain weighted partial copula function. 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 certain (high-level) conditions (on the estimated conditional marginals), rates of convergence for the weighted partial copula process and the test statistic as well as the weak convergence under the null of the normalized test statistic are established. These high-level conditions on the estimated margins are shown to be valid in a variety of examples ranging from nonparametric kernel to linear quantile regression estimates. 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.