What does Neyman orthogonality protect against?

Question: Let ψ(W; θ, η) be a score function for a target parameter θ and nuisance parameter η. What does Neyman orthogonality at the true nuisance value η₀ require? A) The score must be statistically independent of every nuisance estimate B) The derivative of the expected score with respect to local perturbations of η must vanish at η₀ C) The Hessian of the empirical loss with respect to θ and η must be block diagonal D) The nuisance parameter must converge at the same root-n rate as θ Correct: B Explanation: Neyman orthogonality means that the expected moment condition is locally insensitive, to first order, to errors in the nuisance estimate. Consequently, sufficiently small nuisance-estimation errors influence the target estimator mainly through higher-order terms. Orthogonality does not imply independence, a block-diagonal Hessian, or root-n convergence of every nuisance model. Topic: advanced ML / causal inference / double machine learning