No-harm calibration for generalized Oaxaca-Blinder estimators
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In randomized experiments, linear regression with baseline features can be used to form an estimate of the sample average treatment effect that is asymptotically no less efficient than the treated-minus-control difference in means. Randomization alone provides this "do-no-harm" property, with neither truth of a linear model nor a generative model for the outcomes being required. We present a general calibration step which confers the same no-harm property onto estimators leveraging a broad class of nonlinear models. The process recovers the usual regression-adjusted estimator when ordinary least squares is used, and further provides non-inferior treatment effect estimators using methods such as logistic and Poisson regression. The resulting estimators are non-inferior with respect to both the difference in means estimator and with respect to treatment effect estimators that have not undergone calibration.
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