A1316
Title: Efficiency and robustness of Rosenbaum's rank-based estimator in randomized experiments
Authors: Nabarun Deb - University of Chicago (United States) [presenting]
Bikram Karmakar - University of Florida (United States)
Aditya Ghosh - Stanford University (United States)
Bodhisattva Sen - Columbia University (United States)
Abstract: Mean-based estimators of the causal effect in a completely randomized experiment may behave poorly if the potential outcomes have a heavy tail or contain outliers. An alternative estimator is studied by Rosenbaum that estimates the constant additive treatment effect by inverting a randomization test using ranks. By investigating the breakdown point and asymptotic relative efficiency of this rank-based estimator, it is shown that it is provably robust against outliers and heavy-tailed potential outcomes and has asymptotic variance at most 1.16 times that of the difference-in-means estimator (and much smaller when the potential outcomes are not light-tailed). A consistent estimator of the asymptotic standard error is further derived for Rosenbaum's estimator, which yields a readily computable confidence interval for the treatment effect. A regression-adjusted version of Rosenbaum's estimator is also studied to incorporate additional covariate information in randomization inference. The gain in efficiency is proven by this regression adjustment method under a linear regression model. It is illustrated through synthetic and real data that, unlike the mean-based estimators, these rank-based estimators (unadjusted or regression-adjusted) are efficient and robust against heavy-tailed distributions, contamination, and model misspecification. Finally, the study of Rosenbaum's estimator is initiated when the constant treatment effect assumption may be violated.
