The Fundamental Limits of Structure-Agnostic Functional Estimation

Understand

Many recent developments in causal inference, and functional estimation problems more generally, have been motivated by the fact that classical one-step (first-order) debiasing methods, or their more recent sample-split double machine-learning avatars, can outperform plugin estimators under surprisingly weak conditions.

• These first-order corrections improve on plugin estimators in a black-box fashion, and consequently are often used in conjunction with powerful off-the-shelf estimation methods.
• These first-order methods are however provably suboptimal in a minimax sense for functional estimation when the nuisance functions live in Holder-type function spaces.
• This suboptimality of first-order debiasing has motivated the development of "higher-order" debiasing methods.