Lin Liu, Rajarshi Mukherjee, James M Robins
arXiv 21 Jun 2026 · Mathematics — Statistics Theory
arXiv:2606.22391 · PDF · DOI · OpenAlex · Extracted main text
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.
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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 | Sivaraman Balakrishnan, Edward H Kennedy, and Larry Wasserman (2026) The fundamental limits of structure-agnostic functional estimation | 1.000 | 23 | 6 | 100% |
| 2 | Lin Liu, Rajarshi Mukherjee, and James M Robins (2020) On nearly assumption-free tests of nominal confidence interval coverage for causal parameters estimated by machine learning self | 1.000 | 9 | 5 | 100% |
| 3 | Lin Liu, Rajarshi Mukherjee, and James M Robins (2024) Assumption-lean falsification tests of rate double-robustness of double-machine-learning estimators self | 1.000 | 7 | 5 | 100% |
| 4 | Lin Liu, Rajarshi Mukherjee, Whitney K Newey, and James M Robins (2017) Semiparametric efficient empirical higher order influence function estimators self | 1.000 | 5 | 4 | 100% |
| 5 | James M Robins and Ya'acov Ritov (1997) Toward a curse of dimensionality appropriate (CODA) asymptotic theory for semi-parametric models self | 1.000 | 5 | 3 | 100% |
| 6 | Jikai Jin and Vasilis Syrgkanis (2025) Structure-agnostic optimality of doubly robust learning for treatment effect estimation | 0.928 | 4 | 4 | 100% |
| 7 | Andrea Rotnitzky, Ezequiel Smucler, and James M Robins (2021) Characterization of parameters with a mixed bias property self | 0.843 | 3 | 3 | 100% |
| 8 | Ya'acov Ritov, Peter J Bickel, Anthony C Gamst, and Bastiaan Jan Kor… (2014) The Bayesian analysis of complex, high-dimensional models: Can it be CODA? | 0.737 | 3 | 2 | 100% |
| 9 | James Robins, Lingling Li, Eric Tchetgen Tchetgen, and Aad van der V… (2008) Higher order influence functions and minimax estimation of nonlinear functionals self | 0.737 | 3 | 2 | 100% |
| 10 | James Robins, Lingling Li, Eric Tchetgen Tchetgen, and Aad van der V… (2016) Technical report: Higher order influence functions and minimax estimation of nonlinear functionals self | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 45 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Stabilized Higher-Order Influence Functions: Statistical Theory of a Class of Bilinear Forms | 0.405 | 1 | 1 |