Structure-agnostic Optimality of Doubly Robust Learning for Treatment Effect Estimation
CoRR(2024)
摘要
Average treatment effect estimation is the most central problem in causal
inference with application to numerous disciplines. While many estimation
strategies have been proposed in the literature, recently also incorporating
generic machine learning estimators, the statistical optimality of these
methods has still remained an open area of investigation. In this paper, we
adopt the recently introduced structure-agnostic framework of statistical lower
bounds, which poses no structural properties on the nuisance functions other
than access to black-box estimators that attain small errors; which is
particularly appealing when one is only willing to consider estimation
strategies that use non-parametric regression and classification oracles as a
black-box sub-process. Within this framework, we prove the statistical
optimality of the celebrated and widely used doubly robust estimators for both
the Average Treatment Effect (ATE) and the Average Treatment Effect on the
Treated (ATTE), as well as weighted variants of the former, which arise in
policy evaluation.
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