# On the Asymptotic Inadmissibility of Double Machine Learning Estimators Under Structure-Agnostic Models

arXiv: https://arxiv.org/abs/2606.22391 · HTML: https://mlsanity.com/paper/2606.22391/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 46 references that are in the map.
- First posted on arXiv 21 Jun 2026.

## Builds on (most cited first, 17 of 17)

- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [The gap between theory and practice in function approximation with deep neural networks](https://mlsanity.com/paper/2001.07523/) (2020)
- [Universal Inference](https://mlsanity.com/paper/1912.11436/) (2019)
- [The Fundamental Limits of Structure-Agnostic Functional Estimation](https://mlsanity.com/paper/2305.04116/) (2023)
- [DeepMed: Semiparametric Causal Mediation Analysis with Debiased Deep Learning](https://mlsanity.com/paper/2210.04389/) (2022)
- [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)
- [Doubly-robust inference and optimality in structure-agnostic models with smoothness](https://mlsanity.com/paper/2405.08525/) (2024)
- [Structure-agnostic Optimality of Doubly Robust Learning for Treatment Effect Estimation](https://mlsanity.com/paper/2402.14264/) (2024)
- [It's Hard to Be Normal: The Impact of Noise on Structure-agnostic Estimation](https://mlsanity.com/paper/2507.02275/) (2025)
- [Adaptive, Rate-Optimal Hypothesis Testing in Nonparametric IV Models](https://mlsanity.com/paper/2006.09587/) (2020)
- [Nuisance Function Tuning and Sample Splitting for Optimally Estimating a Doubly Robust Functional](https://mlsanity.com/paper/2212.14857/) (2022)
- [Optimally taming biases in black-box models for efficient semiparametric estimation](https://mlsanity.com/paper/2606.06368/) (2026)
- [Discussion of "On nearly assumption-free tests of nominal confidence interval coverage for causal parameters estimated by machine learning"](https://mlsanity.com/paper/2006.09613/) (2020)
- [Assumption-lean falsification tests of rate double-robustness of double-machine-learning estimators](https://mlsanity.com/paper/2306.10590/) (2023)
- [Double Cross-fit Doubly Robust Estimators: Beyond Series Regression](https://mlsanity.com/paper/2403.15175/) (2024)
- [Perturbed Double Machine Learning: Nonstandard Inference Beyond the Parametric Length](https://mlsanity.com/paper/2511.01222/) (2025)

## Built on by (most cited first, 3 of 3)

- [Stabilized Higher-Order Influence Functions: Statistical Theory of a Class of Bilinear Forms](https://mlsanity.com/paper/2607.04743/) (2026)
- [Analytical and Bootstrap Confidence Intervals for Double Machine Learning: Simulation Studies and an Application to Rural-Urban Differences in Obesity Prevalence](https://mlsanity.com/paper/2607.29456/) (2026)
- [Sharp Structure-Agnostic Minimax Risk for Partial Linear Models](https://mlsanity.com/paper/2609.07997/) (2026)

## Abstract (arXiv)

Structure-agnostic (SA) models introduced by Balakrishnan et al. (2026) aim to reflect the general lack of knowledge of structural assumptions on data-generating laws such as smoothness or sparsity in practice. Roughly speaking, SA models restrict the observed-data generating law to be in some rn-neighborhood of (black-box machine learning) estimates, treated as given and fixed, where rn encodes the convergence rates of the estimates to the truth. Under SA models, Balakrishnan et al. (2026) show that the popular Double Machine Learning (DML) estimators for three functionals, the quadratic functional in the Gaussian sequence model, the quadratic density integral functional and the expected conditional covariance, are minimax. However, minimax estimators may be inadmissible. In this paper, we show that, for the first two of the three functionals, the DML estimator is asymptotically inadmissible under the SA model. In particular, we show that these two functionals fall into a class of functionals, which we refer to as the monotone bias class. For this class, we exhibit second-order (U-statistic) estimators, which asymptotically dominate DML estimators, under the SA model. These second-order estimators are empirical higher-order influence function (HOIF) estimators introduced in Liu et al. (2017). Furthermore, the empirical HOIF estimator, like the DML estimator, is minimax for the third functional (the expected conditional covariance), although neither asymptotically dominates the other.