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Abstract:
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The excellent statistical properties of linear estimators are well known. For example, under Gaussian noise, a result of Donoho [1994] guarantees that minimax linear estimators are nearly minimax among all estimators for estimating a linear functional of a parameter only known to belong to a convex class. In this talk, I'll discuss augmenting minimax linear estimators with a non-parametric regression adjustment, and show how the resulting (non-linear) method can improve over asymptotic guarantees available for linear estimation. In particular, we provide general conditions under which augmented minimax linear estimators are semiparametrically efficient; these conditions not only hold for appropriate convex parameter classes, but also allow for non-convex sparsity classes. We discuss the application of our approach to several estimands motivated by causal inference, including several notions of the average treatment effect for continuous treatments. In simulations, we observe promising performance relative to existing methods.
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