Lin Liu, Rajarshi Mukherjee, James M. Robins
arXiv 18 Jun 2023 · Statistics — Methodology · publishedJournal of Econometrics (2023) · 6 citations (OpenAlex)
arXiv:2306.10590 · PDF · DOI · OpenAlex · Extracted main text
The class of doubly-robust (DR) functionals studied by Rotnitzky et al. (2021) is 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. (2022b) and (ii) the class of functionals studied by Robins et al. (2008). The present state-of-the-art estimators for DR functionals $\psi$ are double-machine-learning (DML) estimators (Chernozhukov et al., 2018). A DML estimator $\widehat{\psi}_{1}$ of $\psi$ depends on estimates $\widehat{p} (x)$ and $\widehat{b} (x)$ of a pair of nuisance functions $p(x)$ and $b(x)$, and is said to satisfy "rate double-robustness" if the Cauchy--Schwarz upper bound of its bias is $o (n^{- 1/2})$. Were it achievable, our scientific goal would have been to construct valid, assumption-lean (i.e. no complexity-reducing assumptions on $b$ or $p$) tests of 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 to be $o (n^{-1/2})$, which can be shown not to exist. We therefore adopt the less ambitious goal of falsifying, when possible, an analyst's justification for her claim that the reported $(1 - \alpha)$ Wald CI is valid. In many instances, an analyst 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", with non-trivial power against certain alternatives. If $H_{0}$ is rejected, we will have falsified her justification. However, no assumption-lean test of $H_{0}$, including ours, can be a consistent test. Thus, the failure of our test to reject is not meaningful evidence in favor of $H_{0}$.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Liu, Lin, Mukherjee, Rajarshi, Robins, James M (2020) On nearly assumption-free tests of nominal confidence interval coverage for causal parameters estimated by machine learning self | 1.000 | 11 | 4 | 100% |
| 2 | Liu, Lin, Mukherjee, Rajarshi, Newey, Whitney K, Robins, James M (2017) Semiparametric efficient empirical higher order influence function estimators self | 0.928 | 5 | 5 | 80% |
| 3 | Ai, Chunrong, Chen, Xiaohong (2003) Efficient estimation of models with conditional moment restrictions containing unknown functions | 0.928 | 5 | 3 | 80% |
| 4 | Rotnitzky, Andrea, Smucler, Ezequiel, Robins, James M (2021) Characterization of parameters with a mixed bias property self | 0.909 | 16 | 4 | 75% |
| 5 | Chernozhukov, Victor, Chetverikov, Denis, Demirer, Mert, Duflo, Esth… (2018) Double/debiased machine learning for treatment and structural parameters self | 0.874 | 8 | 2 | 100% |
| 6 | Newey, Whitney K, Robins, James M (2018) Cross-fitting and fast remainder rates for semiparametric estimation self | 0.874 | 6 | 2 | 100% |
| 7 | Ai, Chunrong, Chen, Xiaohong (2007) Estimation of possibly misspecified semiparametric conditional moment restriction models with different conditioning variables | 0.843 | 4 | 3 | 75% |
| 8 | Kline, Patrick, Saggio, Raffaele (2020) Leave-out estimation of variance components | 0.843 | 3 | 3 | 100% |
| 9 | Robins, James, Li, Lingling, Tchetgen Tchetgen, Eric, Vaart, Aad (2008) Higher order influence functions and minimax estimation of nonlinear functionals self | 0.814 | 13 | 3 | 54% |
| 10 | Chernozhukov, Victor, Newey, Whitney K, Singh, Rahul (2022) Automatic debiased machine learning of causal and structural effects | 0.811 | 4 | 2 | 100% |
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