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.

翻译：广义因果效应估计量，包括Mann-Whitney参数与因果净效益，为具有非高斯或多变量结果的随机试验提供了灵活的治疗效应汇总方法。我们针对通过成对对比函数定义的一大类广义因果效应估计量，建立了一个统一的基于设计的回归调整与方差估计推断框架。借助U统计量理论与有限总体渐近理论，我们证明了基于个体对与单位对平均构建的回归估计量具有相合性与渐近正态性，即使工作模型存在误设。因此，这些估计量属于模型辅助而非模型依赖类型。与经典平均处理效应估计量相比，我们证明对于非线性对比函数，协变量调整虽能保持相合性，但无法获得普适的效率保证。在推断方面，我们证明标准的异方差稳健与聚类稳健方差估计量在此设定下通常不相合。作为解决方案，我们证明了一种完全的双向聚类稳健方差估计量——其充分考虑了成对依赖性与反向比较——具有相合性。