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.
Acknowledgments
We are grateful for stimulating discussions with Timothy Armstrong, Vitor Hadad, Guido Imbens, Whitney Newey, Jamie Robins, Florian Stebegg and José Zubizarreta, as well as for comments from seminar participants at several venues. We also thank Guido Imbens for sharing the lottery data with us. We initiated this research while D.H. was a Ph.D. candidate at Columbia University and S.W. was visiting Columbia as a postdoctoral research scientist.
Acknowledgments
We are grateful for stimulating discussions with Timothy Armstrong, Vitor Hadad, Guido Imbens, Whitney Newey, Jamie Robins, Florian Stebegg and José Zubizarreta, as well as for comments from seminar participants at several venues. We also thank Guido Imbens for sharing the lottery data with us. We initiated this research while D.H. was a Ph.D. candidate at Columbia University and S.W. was visiting Columbia as a postdoctoral research scientist.
Citation
David A. Hirshberg. Stefan Wager. "Augmented minimax linear estimation." Ann. Statist. 49 (6) 3206 - 3227, December 2021. https://doi.org/10.1214/21-AOS2080
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