Conditional independence testing via weighted partial copulas and nearest neighbors
This addresses a fundamental statistical problem for researchers and practitioners in fields like causal inference, but it appears incremental as it builds on existing methods.
The paper tackles the problem of conditional independence testing by introducing the weighted partial copula function, resulting in a test with competitive power compared to state-of-the-art methods like kernel-based tests.
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.