Adversarial Estimation of Riesz Representers
This work provides a more robust method for estimating Riesz representers, which is important for accurate causal inference, particularly for researchers and practitioners dealing with complex, nonlinear data.
This paper addresses the estimation of Riesz representers, which are crucial for the asymptotic variance of semiparametrically estimated linear functionals in causal inference. The authors propose an adversarial framework to estimate these representers using various function spaces, achieving nominal coverage in highly nonlinear simulations where prior methods failed.
Many causal parameters are linear functionals of an underlying regression. The Riesz representer is a key component in the asymptotic variance of a semiparametrically estimated linear functional. We propose an adversarial framework to estimate the Riesz representer using general function spaces. We prove a nonasymptotic mean square rate in terms of an abstract quantity called the critical radius, then specialize it for neural networks, random forests, and reproducing kernel Hilbert spaces as leading cases. Our estimators are highly compatible with targeted and debiased machine learning with sample splitting; our guarantees directly verify general conditions for inference that allow mis-specification. We also use our guarantees to prove inference without sample splitting, based on stability or complexity. Our estimators achieve nominal coverage in highly nonlinear simulations where some previous methods break down. They shed new light on the heterogeneous effects of matching grants.