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Mean-based estimators of the causal effect in a completely randomizedexperiment (e.g., the difference-in-means estimator) may behave poorly if thepotential outcomes have a heavy-tail, or contain outliers. We study analternative estimator by Rosenbaum that estimates the constant additivetreatment effect by inverting a randomization test using ranks. Byinvestigating the breakdown point and asymptotic relative efficiency of thisrank-based estimator, we show that it is provably robust against heavy-tailedpotential outcomes, and has variance that is asymptotically, in the worst case,at most about 1.16 times that of the difference-in-means estimator; and itsvariance can be much smaller when the potential outcomes are not light-tailed.We further derive a consistent estimator of the asymptotic standard error forRosenbaum's estimator which yields a readily computable confidence interval forthe treatment effect. Further, we study a regression adjusted version ofRosenbaum's estimator to incorporate additional covariate information inrandomization inference. We prove gain in efficiency by this regressionadjustment method under a linear regression model. We illustrate throughsynthetic and real data that, unlike the mean-based estimators, theserank-based estimators (both unadjusted or regression adjusted) are efficientand robust against heavy-tailed distributions, contamination, and modelmisspecification.

Efficiency and Robustness of Rosenbaum's Regression (Un)-Adjusted Rank-based Estimator in Randomized Experiments