Mean-based estimators of causal effects in randomized experiments may behave poorly if the potential outcomes have a heavy tail or contain outliers. An alternative estimator proposed by Rosenbaum (1993) estimates a constant additive treatment effect by inverting a randomization test using ranks. We develop a design-based asymptotic theory for this rank-based estimator and study its robustness and efficiency properties. We show that Rosenbaum's estimator is robust against outliers with a breakdown point that uniformly dominates that of any weighted quantile estimator. When pretreatment covariates are available, a regression-adjusted version of Rosenbaum's estimator uses an agnostic linear regression on the covariates and bases inference on the ranks of residuals. Under mild integrability conditions, we show that this estimator is at most 13.6% less efficient, in the worst case, than the commonly used mean-based regression adjustment method proposed by Lin (2013); often outperforming it when the residuals have heavy tails. Moreover, under suitable assumptions, Rosenbaum's regression-adjusted estimator is at least as efficient as the unadjusted one. Finally, we initiate the study of Rosenbaum's estimator when the constant treatment effect assumption may be violated. To analyze the regression-adjusted estimator, we develop local asymptotics of rank statistics under the design-based framework, which may be of independent interest.

翻译：在随机化实验中，若潜在结果存在重尾分布或异常值，基于均值的因果效应估计量可能表现不佳。Rosenbaum（1993）提出的替代估计量通过逆用秩随机化检验来估计常数加性处理效应。本文为该秩估计量建立了基于设计的渐近理论，并研究其稳健性与效率性质。我们证明Rosenbaum估计量对异常值具有稳健性，其崩溃点一致优于任何加权分位数估计量。当存在预处理协变量时，Rosenbaum估计量的回归调整版本对协变量进行不可知线性回归，并基于残差秩进行推断。在温和的可积性条件下，我们证明该估计量在最坏情况下比Lin（2013）提出的常用基于均值的回归调整方法至多损失13.6%的效率；当残差呈重尾分布时，其表现通常更优。此外，在适当假设下，Rosenbaum回归调整估计量的效率不低于未调整版本。最后，我们初步研究了常数处理效应假设可能被违反时Rosenbaum估计量的性质。为分析回归调整估计量，我们在基于设计的框架下发展了秩统计量的局部渐近理论，该理论可能具有独立的研究价值。