A Projection Approach to Nonparametric Significance and Conditional Independence Testing

Abstract: This paper develops a novel nonparametric significance test based on a tailored nonparametric-type projected weighting function that exhibits appealing theoretical and numerical properties. We derive the asymptotic properties of the proposed test and show that it can detect local alternatives at the parametric rate. Using the nonparametric orthogonal projection, we construct a computationally convenient multiplier bootstrap to obtain critical values from the case-dependent asymptotic null distribution. Compared with the existing literature, our approach overcomes the need for a stronger compact support assumption on the density of covariates arising from random denominators. We also extend the tailor-made projection procedure to test the conditional independence assumption. The simulation experiments further illustrate the advantages of our proposed method in testing significance and conditional independence in finite samples.