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

arXiv: https://arxiv.org/abs/2306.10590 · HTML: https://mlsanity.com/paper/2306.10590/

## 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.

## Builds on (most cited first, 30 of 36)

- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Intrinsic dimension of data representations in deep neural networks](https://mlsanity.com/paper/1905.12784/) (2019)
- [Neural Networks can Learn Representations with Gradient Descent](https://mlsanity.com/paper/2206.15144/) (2022)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [An Introduction to Proximal Causal Learning](https://mlsanity.com/paper/2009.10982/) (2020)
- [Deep Neural Networks for Estimation and Inference](https://mlsanity.com/paper/1809.09953/) (2018)
- [Semiparametric proximal causal inference](https://mlsanity.com/paper/2011.08411/) (2020)
- [Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approach](https://mlsanity.com/paper/2103.14029/) (2021)
- [Robust Inference on Average Treatment Effects with Possibly More Covariates than Observations](https://mlsanity.com/paper/1309.4686/) (2013)
- [The Influence Function of Semiparametric Estimators](https://mlsanity.com/paper/1508.01378/) (2015)
- [A confounding bridge approach for double negative control inference on causal effects](https://mlsanity.com/paper/1808.04945/) (2018)
- [Adversarial Estimation of Riesz Representers](https://mlsanity.com/paper/2101.00009/) (2020)
- [De-Biased Machine Learning of Global and Local Parameters Using Regularized Riesz Representers](https://mlsanity.com/paper/1802.08667/) (2018)
- [Adaptive wavelet distillation from neural networks through interpretations](https://mlsanity.com/paper/2107.09145/) (2021)
- [Optimal Sup-norm Rates and Uniform Inference on Nonlinear Functionals of Nonparametric IV Regression](https://mlsanity.com/paper/1508.03365/) (2015)
- [Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals with Application to Proximal Causal Inference](https://mlsanity.com/paper/2104.02929/) (2021)
- [A unifying approach for doubly-robust ℓ1 regularized estimation of causal contrasts](https://mlsanity.com/paper/1904.03737/) (2019)
- [Deep Learning Methods for Proximal Inference via Maximum Moment Restriction](https://mlsanity.com/paper/2205.09824/) (2022)
- [The Fundamental Limits of Structure-Agnostic Functional Estimation](https://mlsanity.com/paper/2305.04116/) (2023)
- [The Proximal ID Algorithm](https://mlsanity.com/paper/2108.06818/) (2021)
- [DeepMed: Semiparametric Causal Mediation Analysis with Debiased Deep Learning](https://mlsanity.com/paper/2210.04389/) (2022)
- [Higher Order Tangent Spaces and Influence Functions](https://mlsanity.com/paper/1502.00812/) (2015)
- [Sparsity Double Robust Inference of Average Treatment Effects](https://mlsanity.com/paper/1905.00744/) (2019)
- [Minimax Semiparametric Learning With Approximate Sparsity](https://mlsanity.com/paper/1912.12213/) (2019)
- [Rejoinder: On nearly assumption-free tests of nominal confidence interval coverage for causal parameters estimated by machine learning](https://mlsanity.com/paper/2008.03288/) (2020)
- [Causal Inference of General Treatment Effects using Neural Networks with A Diverging Number of Confounders](https://mlsanity.com/paper/2009.07055/) (2020)
- [Efficient Estimation in NPIV Models: A Comparison of Various Neural Networks-Based Estimators](https://mlsanity.com/paper/2110.06763/) (2021)
- [A New Central Limit Theorem for the Augmented IPW Estimator: Variance Inflation, Cross-Fit Covariance and Beyond](https://mlsanity.com/paper/2205.10198/) (2022)
- [Inference in Linear Regression Models with Many Covariates and Heteroskedasticity](https://mlsanity.com/paper/1507.02493/) (2015)
- [Adaptive, Rate-Optimal Hypothesis Testing in Nonparametric IV Models](https://mlsanity.com/paper/2006.09587/) (2020)

## Built on by (most cited first, 2 of 2)

- [On the Asymptotic Inadmissibility of Double Machine Learning Estimators Under Structure-Agnostic Models](https://mlsanity.com/paper/2606.22391/) (2026)
- [When a High Score Is an Illusion: Certifying Genuine versus Repackaged Forecasting Skill](https://mlsanity.com/paper/2609.19223/) (2026)

## 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.