Augmented minimax linear estimation

By David A. Hirshberg, Stefan Wager. 2017

129 citations recorded by the source corpus.

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.

Subfields: Statistics and Probability

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Citations in the corpus

Minimax Weight and Q-Function Learning for Off-Policy Evaluation (2019, background): “Such a trade-off is relatively well understood in contextual bandits (Kallus, 2020; Hirshberg and Wager, 2017), though extension to sequential decision-making is not obvious.”
Minimal dispersion approximately balancing weights: asymptotic properties and practical considerations (2017, background): “2018; Hirshberg and Wager 2018), and there are valuable theoretical results (e.g., Athey et al. 2018; Hirshberg and Wager 2018; Wong and Chan 2018), important aspects of their theoretical properties and their practical usage remain to be studied.”
Policy Learning With Observational Data (2017, background): “In our setting, the condition below acts as a generalization of the overlap assumption (Hirshberg and Wager, 2018). rates over monotone decision rules without making further assumptions on the distribution of the features X i .”
Matching for Balance (2019, methodology): “Examples of weighting methods for covariate balance include Hainmueller (2012), Imai and Ratkovic (2014), Zubizarreta (2015), Chan et al. (2016), Fan et al. (2016), Zhao and Percival (2017), Athey et al. (2018), Hirshberg and Wager (2018), Zhao (2019), and Wang and Zubizarreta (2017).”
The Balancing Act in Causal Inference (2021, methodology): “A slight generalization of this case is addressed in (Hirshberg & Wager, 2018, see Proof of Theorem 1).”
Incremental causal effects (2019, methodology): “In Hirshberg and Wager (2017), this is achieved under Donsker assumptions, while Chernozhukov et al. (2018) employ a sparsity assumption on either the approximation of the Riesz representer or the approximation to the regression function.”