Double machine learning provides n-consistent estimates of parameters of interest even when high-dimensional or nonparametric nuisance parameters are estimated at an n^{-1/4} 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 n^{-1/4} requirement can be improved to n^{-1/(2k+2)} by employing a k-th order notion of orthogonality that grants robustness to more complex or higher-dimensional nuisance parameters. In the partially linear model setting popular in causal inference, we use Stein's lemma to show that we can construct second-order orthogonal moments if and only if the treatment residual is not normally distributed  . We conclude by demonstrating the robustness benefits of an explicit doubly-orthogonal estimation procedure for treatment effect.
Double machine learning provides n-consistent estimates of parameters of interest even when high-dimensional or nonparametric nuisance parameters are estimated at an n^{-1/4} 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 n^{-1/4} requirement can be improved to n^{-1/(2k+2)} 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 popular in causal inference, we show that we can construct second-order orthogonal moments if and only if the treatment residual is not normally distributed . 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.
R
Neyman-orthogonal
Neyman-orthogonal
R
model
regression
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use Stein's lemma to
A
. Our proof relies on Stein's lemma and may be of independent interest