Many causal and structural 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. Furthermore, we use critical radius theory -- in place of Donsker theory -- to prove asymptotic normality without sample splitting, uncovering a ``complexity-rate robustness'' condition. This condition has practical consequences: inference without sample splitting is possible in several machine learning settings, which may improve finite sample performance compared to sample splitting. Our estimators achieve nominal coverage in highly nonlinear simulations where previous methods break down. They shed new light on the heterogeneous effects of matching grants.

翻译：许多因果与结构参数可表示为潜在回归的线性泛函。在非参数估计线性泛函的渐近方差中，Riesz表示子是关键组成部分。我们提出了一种对抗性框架，利用一般函数空间估计Riesz表示子。我们以称为临界半径的抽象量为基础，证明了非渐近均方误差率，并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典型案例。此外，我们利用临界半径理论（替代Donsker理论）证明了无需样本分割即可实现渐近正态性，揭示了“复杂度-速率鲁棒性”条件。该条件具有实际意义：在多种机器学习场景中无需样本分割即可进行统计推断，相较于样本分割方法可能提升有限样本表现。在先前方法失效的高度非线性模拟中，我们的估计量实现了名义覆盖概率。这些结果为配套拨款的异质性效应提供了新见解。