Augmented Minimax Linear Estimation

TL;DR

This paper introduces a minimax linear correction method for estimating linear functionals of conditional expectations, achieving semiparametric efficiency and demonstrating strong empirical performance.

Contribution

It proposes a novel correction technique for plug-in estimators that improves efficiency in estimating various statistical functionals.

Findings

Method is semiparametrically efficient under weak conditions.

Demonstrates promising results on real and simulated data.

Applicable to average treatment effect and personalized treatments.

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.