Augmented minimax linear estimation
David A. Hirshberg, Stefan Wager
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.
Topics & Concepts
MinimaxEstimatorMathematicsConditional expectationSimple (philosophy)Minimax estimatorFunction (biology)Applied mathematicsMathematical optimizationComputer scienceStatisticsMinimum-variance unbiased estimatorPhilosophyEpistemologyBiologyEvolutionary biologyAdvanced Causal Inference TechniquesStatistical Methods and InferenceStatistical Methods in Clinical Trials