A Projection Approach to Nonparametric Significance and Conditional Independence Testing

2026-02-16

AI Summary

This work addresses a key limitation in existing nonparametric tests for significance and conditional independence, which often rely on the strong assumption that covariate densities have compact support, thereby restricting their applicability. To overcome this, the authors propose a weighted function approach based on nonparametric orthogonal projections, coupled with a computationally efficient multiplier bootstrap procedure to accurately estimate critical values. The framework is further extended to conditional independence testing. By relaxing the compact support requirement, the method achieves parametric-rate detection power against local alternatives under more general density conditions. Finite-sample experiments demonstrate that the proposed approach substantially improves both the accuracy and stability of hypothesis testing compared to existing methods.

Technology Category

• Search and Optimization: Non-convex Optimization
• Machine Learning: Kernel Methods
• Reasoning under Uncertainty: Graphical Models

Application Category

• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• nonparametric testing
• significance testing
• conditional independence
• projection method
• asymptotic properties

Innovation

• nonparametric projection
• significance testing
• conditional independence
• multiplier bootstrap
• asymptotic properties