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The class of doubly-robust (DR) functionals studied by Rotnitzky et al.(2021) is of central importance in economics and biostatistics. It strictlyincludes both (i) the class of mean-square continuous functionals that can bewritten as an expectation of an affine functional of a conditional expectationstudied by Chernozhukov et al. (2022b) and (ii) the class of functionalsstudied by Robins et al. (2008). The present state-of-the-art estimators for DRfunctionals $\psi$ are double-machine-learning (DML) estimators (Chernozhukovet al., 2018). A DML estimator $\widehat{\psi}_{1}$ of $\psi$ depends onestimates $\widehat{p} (x)$ and $\widehat{b} (x)$ of a pair of nuisancefunctions $p(x)$ and $b(x)$, and is said to satisfy "rate double-robustness" ifthe Cauchy--Schwarz upper bound of its bias is $o (n^{- 1/2})$. Were itachievable, our scientific goal would have been to construct valid,assumption-lean (i.e. no complexity-reducing assumptions on $b$ or $p$) testsof the validity of a nominal $(1 - \alpha)$ Wald confidence interval (CI)centered at $\widehat{\psi}_{1}$. But this would require a test of the bias tobe $o (n^{-1/2})$, which can be shown not to exist. We therefore adopt the lessambitious goal of falsifying, when possible, an analyst's justification for herclaim that the reported $(1 - \alpha)$ Wald CI is valid. In many instances, ananalyst justifies her claim by imposing complexity-reducing assumptions on $b$and $p$ to ensure "rate double-robustness". Here we exhibit valid,assumption-lean tests of $H_{0}$: "rate double-robustness holds", withnon-trivial power against certain alternatives. If $H_{0}$ is rejected, we willhave falsified her justification. However, no assumption-lean test of $H_{0}$,including ours, can be a consistent test. Thus, the failure of our test toreject is not meaningful evidence in favor of $H_{0}$.

Assumption-lean falsification tests of rate double-robustness of double-machine-learning estimators