Neyman orthogonality

Debiased machine learning (DML) is a generic recipe. The idea behind it is adding a correction term to the plug-in estimator of the functional, which leads to properties such as semi-parametric efficiency, double robustness, and Neyman orthogonality.

The following exercise is from CausalAIBook Notebook. The goal is to illustrate the difference between Neyman orthogonal vs non-orthogonal approach. Setting We compare the performance of the naive and orthogonal methods in a computational experiment where $p=n=100$, ${\beta }_j=1/j^2$, $({\gamma }_{DW}{)}_j=1/j^2$ and $$Y=1\cdot D+{\beta }^{\prime }W+{ϵ}_Y$$

Motivation & Intuition In classical semiparametric theory, we want to estimate a low‑dimensional target parameter (say, a treatment effect) while controlling for high‑dimensional nuisance functions (like nonparametric regressions). However, in order to use the central limit theorem (CLT) and to characterize the asymptotic behavior, classical results require that the space of functions in which these nuisance functions lie is “small” in a technical sense.