Design-based inference for generalized causal effects in randomized experiments

2026-02-20

AI Summary

This study addresses the lack of a unified robust inference framework for generalized causal effects—such as the Mann-Whitney parameter or causal net benefit—under non-Gaussian or multivariate outcomes. The authors develop a design-based regression adjustment and variance estimation framework that defines effect sizes through pairwise contrast functions. Innovatively integrating U-statistics with finite-population asymptotic theory, they propose a model-assisted (rather than model-dependent) estimation approach and demonstrate that covariate adjustment does not universally yield efficiency gains under nonlinear contrasts. To resolve the inconsistency of existing robust variance estimators in this setting, they further introduce a fully two-way clustered robust variance estimator. Theoretical analysis establishes the consistency and asymptotic normality of the proposed estimators, which remain valid even under misspecification of the working model.

Technology Category

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

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Generalized causal effect estimands, including the Mann-Whitney parameter and causal net benefit, provide flexible summaries of treatment effects in randomized experiments with non-Gaussian or multivariate outcomes. We develop a unified design-based inference framework for regression adjustment and variance estimation of a broad class of generalized causal effect estimands defined through pairwise contrast functions. Leveraging the theory of U-statistics and finite-population asymptotics, we establish the consistency and asymptotic normality of regression estimators constructed from individual pairs and per-unit pair averages, even when the working models are misspecified. Consequently, these estimators are model-assisted rather than model-based. In contrast to classical average treatment effect estimands, we show that for nonlinear contrast functions, covariate adjustment preserves consistency but does not admit a universal efficiency guarantee. For inference, we demonstrate that standard heteroskedasticity-robust and cluster-robust variance estimators are generally inconsistent in this setting. As a remedy, we prove that a complete two-way cluster-robust variance estimator, which fully accounts for pairwise dependence and reverse comparisons, is consistent.

Problem

• generalized causal effects
• randomized experiments
• regression adjustment
• variance estimation
• U-statistics

Innovation

• design-based inference
• generalized causal effects
• regression adjustment
• U-statistics
• cluster-robust variance