Augmented minimax linear estimation
David A. Hirshberg, Stefan Wager
The Annals of Statistics · 2021 · Volume 49 · Issue 6
Abstract
Many statistical estimands can expressed as continuous linear functionals of a conditional expectation function. This includes the average treatment effect under unconfoundedness and generalizations for continuous-valued and personalized treatments. In this paper, we discuss a general approach to estimating such quantities: we begin with a simple plug-in estimator based on an estimate of the conditional expectation function, and then correct the plug-in estimator by subtracting a minimax linear estimate of its error. We show that our method is semiparametrically efficient under weak conditions and observe promising performance on both real and simulated data.
Keywords
62F12, Causal inference, Convex optimization, Semiparametric efficiency
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