Conditional Independence Testing for General Sufficient Dimension Reduction Methods

Abstract

We study conditional independence testing within the sufficient dimension reduction (SDR) framework. The goal is to assess whether selected predictors contribute to explaining the response after controlling for the others, with SDR alleviating the curse of dimensionality and preserving modeling flexibility. We propose a novel procedure that performs conditional independence testing by combining appropriate residualization with SDR dimension testing. The procedure is adaptable to a broad class of SDR methods, allowing the direct application of existing dimension tests. Simulations show our procedure achieves empirical performance comparable or superior to that of existing methods in several settings.

Keywords: Conditional independence test, Coordinate test, Dimension test, Residualization, Sufficient dimension reduction