Double cross-fit doubly robust estimators: Beyond series regression

Abstract Double cross-fit doubly robust (DCDR) estimators, which train nuisance function estimators on separate samples, are effective new estimators for causal functionals. We establish several novel theoretical results for them, building on recent work. We provide a structure-agnostic error analysis, which holds with generic nuisance functions and estimators. Then, we propose n-consistent DCDR estimators with undersmoothed local polynomial regression and k-Nearest Neighbours and a minimax rate-optimal DCDR estimator with undersmoothed kernel regression. Finally, we demonstrate inference is possible even in the non-root-n regime with a central limit theorem for an undersmoothed DCDR estimator. We reinforce our theoretical results with simulation experiments.