Assumption-lean falsification tests of rate double-robustness of double-machine-learning estimators
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Abstract (arXiv)
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 widehatpsi1 of psi depends on estimates widehatp (x) and widehatb (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 - α) Wald confidence interval (CI) centered at widehatpsi1. 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 - α) 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 H0: "rate double-robustness holds", with non-trivial power against certain alternatives. If H0 is rejected, we will have falsified her justification. However, no assumption-lean test of H0, including ours, can be a consistent test. Thus, the failure of our test to reject is not meaningful evidence in favor of H0.
Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 36 of its 95 references that are in the map. First posted on arXiv 18 Jun 2023.
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References · 36
- 2017Nonparametric regression using deep neural networks with ReLU activation functioncited by 433
- 2019Intrinsic dimension of data representations in deep neural networkscited by 282
- 2022Neural Networks can Learn Representations with Gradient Descentcited by 161
- 2016Identifying Causal Effects With Proxy Variables of an Unmeasured Confoundercited by 139
- 2020An Introduction to Proximal Causal Learningcited by 95
- 2018Deep Neural Networks for Estimation and Inferencecited by 62
- 2020Semiparametric proximal causal inferencecited by 59
- 2021Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approachcited by 44
- 2013Robust Inference on Average Treatment Effects with Possibly More Covariates than Observationscited by 38
- 2015The Influence Function of Semiparametric Estimatorscited by 36
- 2018A confounding bridge approach for double negative control inference on causal effectscited by 36
- 2020Adversarial Estimation of Riesz Representerscited by 35
24 more
- 2018De-Biased Machine Learning of Global and Local Parameters Using Regularized Riesz Representerscited by 34
- 2021Adaptive wavelet distillation from neural networks through interpretationscited by 32
- 2015Optimal Sup-norm Rates and Uniform Inference on Nonlinear Functionals of Nonparametric IV Regressioncited by 30
- 2021Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals with Application to Proximal Causal Inferencecited by 20
- 2019A unifying approach for doubly-robust ℓ1 regularized estimation of causal contrastscited by 15
- 2022Deep Learning Methods for Proximal Inference via Maximum Moment Restrictioncited by 14
- 2023The Fundamental Limits of Structure-Agnostic Functional Estimationcited by 12
- 2021The Proximal ID Algorithmcited by 11
- 2022DeepMed: Semiparametric Causal Mediation Analysis with Debiased Deep Learningcited by 10
- 2015Higher Order Tangent Spaces and Influence Functionscited by 9
- 2019Sparsity Double Robust Inference of Average Treatment Effectscited by 7
- 2019Minimax Semiparametric Learning With Approximate Sparsitycited by 7
- 2020Rejoinder: On nearly assumption-free tests of nominal confidence interval coverage for causal parameters estimated by machine learningcited by 7
- 2020Causal Inference of General Treatment Effects using Neural Networks with A Diverging Number of Confounderscited by 7
- 2021Efficient Estimation in NPIV Models: A Comparison of Various Neural Networks-Based Estimatorscited by 5
- 2022A New Central Limit Theorem for the Augmented IPW Estimator: Variance Inflation, Cross-Fit Covariance and Beyondcited by 5
- 2015Inference in Linear Regression Models with Many Covariates and Heteroskedasticitycited by 4
- 2020Adaptive, Rate-Optimal Hypothesis Testing in Nonparametric IV Modelscited by 4
- 2022Nuisance Function Tuning and Sample Splitting for Optimally Estimating a Doubly Robust Functionalcited by 3
- 2013Optimal Uniform Convergence Rates for Sieve Nonparametric Instrumental Variables Regressioncited by 2
- 2018Two-Step Estimation and Inference with Possibly Many Included Covariatescited by 2
- 2020Discussion of "On nearly assumption-free tests of nominal confidence interval coverage for causal parameters estimated by machine learning"cited by 2
- 2022Explaining Practical Differences Between Treatment Effect Estimators with High Dimensional Asymptoticscited by 2
- 2021Simple Adaptive Estimation of Quadratic Functionals in Nonparametric IV Modelscited by 1
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