Conditional independence testing via weighted partial copulas and nearest neighbors

TL;DR

This paper proposes a new statistical test for conditional independence using weighted partial copulas and nearest neighbors, with theoretical guarantees and competitive empirical performance.

Contribution

It introduces the weighted partial copula function and a bootstrap-based testing procedure, advancing conditional independence testing methods.

Findings

The test has competitive power compared to state-of-the-art methods.

Weak convergence of the weighted partial copula process is established.

The method effectively mimics conditional independence through bootstrap sampling.

Abstract

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.