A general nonparametric framework for testing hypotheses about function-valued parameters

2026-04-21

AI Summary

This study addresses the fundamental question of whether a statistical parameter defined through a conditional distribution remains constant across covariates—a problem encompassing treatment effect heterogeneity and conditional association. The authors propose a general nonparametric testing framework based on smooth functionals applied to conditional distributions, yielding functional parameters for which they construct test statistics with tractable asymptotic distributions. Their approach explicitly links to norm-based tests in function spaces and, compared to existing norm-type methods, exhibits superior asymptotic properties under the null hypothesis. Simulation studies demonstrate strong finite-sample performance, and the method is successfully applied to data from a breast cancer clinical trial, effectively identifying key biomarkers predictive of response to adjuvant chemotherapy.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Non-convex Optimization
• Reasoning under Uncertainty: Graphical Models

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

We present a general nonparametric approach for testing whether a statistical parameter defined through conditional distributions is constant across the conditioning variables. Such hypotheses arise naturally in problems such as assessing treatment effect heterogeneity, conditional associational effects, and conditional mean dependence. Our framework studies function-valued parameters obtained by evaluating a smooth statistical functional on conditional probability distributions. We establish an explicit connection between our test and procedures based on studying the norm of the function-valued parameter. Unlike many existing norm-based tests, which exhibit poor asymptotic behavior under the null, the proposed test statistic admits a tractable limiting null distribution. We illustrate the applicability of the proposed test through several examples, assess its operating characteristics in simulation studies, and apply it to data from a breast cancer trial to identify predictive biomarkers for response to adjuvant chemotherapy.

Problem

• function-valued parameters
• nonparametric testing
• conditional distributions
• hypothesis testing
• treatment effect heterogeneity

Innovation

• nonparametric testing
• function-valued parameters
• conditional distributions
• treatment effect heterogeneity
• limiting null distribution