In this article we develop a feasible version of the assumption-lean tests in Liu et al. 20 that can falsify an analyst's justification for the validity of a reported nominal $(1 - \alpha)$ Wald confidence interval (CI) centered at a double machine learning (DML) estimator for any member of the class of doubly robust (DR) functionals studied by Rotnitzky et al. 21. The class of DR functionals is broad and of central importance in economics and biostatistics. It strictly includes both (i) the class of mean-square continuous functionals that can be written as an expectation of an affine functional of a conditional expectation studied by Chernozhukov et al. 22 and the class of functionals studied by Robins et al. 08. The present state-of-the-art estimators for DR functionals $\psi$ are DML estimators $\hat{\psi}_{1}$. The bias of $\hat{\psi}_{1}$ depends on the product of the rates at which two nuisance functions $b$ and $p$ are estimated. Most commonly an analyst justifies the validity of her Wald CIs by proving that, under her complexity-reducing assumptions, the Cauchy-Schwarz (CS) upper bound for the bias of $\hat{\psi}_{1}$ is $o (n^{- 1 / 2})$. Thus if the hypothesis $H_{0}$: the CS upper bound is $o (n^{- 1 / 2})$ is rejected by our test, we will have falsified the analyst's justification for the validity of her Wald CIs. In this work, we exhibit a valid assumption-lean falsification test of $H_{0}$, without relying on complexity-reducing assumptions on $b, p$, or their estimates $\hat{b}, \hat{p}$. Simulation experiments are conducted to demonstrate how the proposed assumption-lean test can be used in practice. An unavoidable limitation of our methodology is that no assumption-lean test of $H_{0}$, including ours, can be a consistent test. Thus failure of our test to reject is not meaningful evidence in favor of $H_{0}$.

翻译：[摘要] 本文针对Liu等人（2020）提出的假设简约检验方法，开发了一种可行版本。该检验可证伪分析者对其报告的名义$(1 - \alpha)$Wald置信区间（CI）有效性的论证依据——该区间以Rotnitzky等人（2021）研究的双重稳健泛函类中任意成员的双重机器学习（DML）估计量为中心。该双重稳健泛函类具有广泛性，在经济学和生物统计学中具有核心重要性，严格包含：（i）Chernozhukov等人（2022）研究的可表示为条件期望仿射泛函期望的均方连续泛函类，以及（ii）Robins等人（2008）研究的泛函类。当前针对双重稳健泛函$\psi$的最先进估计量是DML估计量$\hat{\psi}_{1}$。$\hat{\psi}_{1}$的偏差取决于两个干扰函数$b$和$p$估计速率的乘积。通常，分析者通过证明在其复杂度简化假设下，$\hat{\psi}_{1}$偏差的柯西-施瓦茨（CS）上界为$o (n^{- 1 / 2})$，来论证其Wald置信区间的有效性。因此，若我们的检验拒绝原假设$H_{0}$（即CS上界为$o (n^{- 1 / 2})$），则证伪了分析者对其Wald置信区间有效性的论证依据。本工作展示了一个有效的假设简约证伪检验，该检验无需依赖对$b$、$p$或其估计量$\hat{b}$、$\hat{p}$的复杂度简化假设。通过模拟实验展示了所提出的假设简约检验在实际中的应用。本方法存在一个不可避免的局限：任何对$H_{0}$的假设简约检验（包括本检验）均无法保证一致性。因此，本检验未拒绝原假设并不构成支持$H_{0}$的有效证据。