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.

翻译：许多因果参数是潜在回归的线性泛函。Riesz表示量是半参数估计线性泛函渐近方差中的关键组成部分。我们提出一个对抗性框架，利用一般函数空间估计Riesz表示量。我们证明了一个以临界半径这一抽象量表示的非渐近均方速率，随后将其专门应用于神经网络、随机森林和再生核希尔伯特空间等主要情形。我们的估计量与带有样本分裂的有针对性和去偏机器学习高度兼容；我们的保证直接验证了允许错误设定的推断一般条件。我们还利用基于稳定性或复杂性的保证，证明了无需样本分裂的推断。在高度非线性的模拟中，我们的估计量实现了名义覆盖，而一些先前的方法在此类模拟中失效了。它们为配套补助金的异质性效应提供了新的见解。