Abstract

Double machine learning provides -consistent estimates of parameters of interest even when high-dimensional or nonparametric nuisance parameters are estimated at an rate. The key is to employ Neyman-orthogonal moment equations which are first-order insensitive to perturbations in the nuisance parameters. We show that the requirement can be improved to by employing a k-th order notion of orthogonality that grants robustness to more complex or higher-dimensional nuisance parameters. In the partially linear regression setting, popula in causal inference, we show that we can construct second-order orthogonal moments if and only if the treatment residual is not normally dis tributed. Our proof relies on Stein’s lemma and may be of independent interest. We conclude by demonstrating the robustness benefits of an explicit doubly-orthogonal estimation procedure for treatment effect.