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What is Learnable in Valiant's Theory of the Learnable? 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The Generalized Oaxaca-Blinder Estimator
Kevin Guo, Guillaume Basse · 2020-04-24 · via math.ST updates on arXiv.org

After performing a randomized experiment, researchers often use ordinary-least squares (OLS) regression to adjust for baseline covariates when estimating the average treatment effect. It is widely known that the resulting confidence interval is valid even if the linear model is misspecified. In this paper, we generalize that conclusion to covariate adjustment with nonlinear models. We introduce an intuitive way to use any "simple" nonlinear model to construct a covariate-adjusted confidence interval for the average treatment effect. The confidence interval derives its validity from randomization alone, and when nonlinear models fit the data better than linear models, it is narrower than the usual interval from OLS adjustment.

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