Generalized projection tests for function-valued parameters with applications to testing structural causal assumptions

2026-03-13

AI Summary

This work proposes a generalized projection test based on series estimation for evaluating structural causal assumptions, which often reduce to testing whether certain functional parameters are zero. The method is tailored for causal inference settings such as data fusion and instrumental variable analysis, and it accommodates flexible machine learning techniques for estimating nuisance parameters. Under the null hypothesis, the limiting distribution of the test statistic is analytically tractable, substantially reducing computational complexity compared to existing approaches while remaining compatible with modern machine learning tools. The effectiveness and practical utility of the proposed test are demonstrated through its successful application in the COVAIL trial, where it was used to assess the equality of conditional COVID-19 risk across different vaccine groups.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Intelligent Robots: State Estimation

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Structural assumptions are central to the causal inference literature. In practice, it is often crucial to assess their validity or to test implications that follow from them. In many settings, such tests can be framed as evaluating whether a function-valued parameter equals zero. In this paper, we propose a class of generalized projection tests based on series estimators for function-valued parameters. We establish conditions under which the proposed tests are valid and illustrate their applicability through examples from the data fusion and instrumental variables literature. Our approach accommodates flexible machine learning methods for estimating nuisance parameters. In contrast to many existing approaches, the limiting distribution of the proposed test statistics is straightforward to compute under the null hypothesis. We apply our method to test the equality of conditional COVID-19 risk across vaccine arms in the COVID-19 Variant Immunologic Landscape (COVAIL) trial.

Problem

• structural causal assumptions
• function-valued parameters
• hypothesis testing
• causal inference
• null hypothesis

Innovation

• generalized projection tests
• function-valued parameters
• causal inference
• series estimators
• machine learning nuisance estimation