Yulin Zhang, Lin Liu, Zheng Zhang
arXiv 1 Jun 2026 · Econometrics
arXiv:2606.01706 · PDF · DOI · OpenAlex · Extracted main text
It is now well known that estimators based on influence functions can be sub-optimal in terms of convergence rates in various settings. To address this issue, higher-order influence functions (HOIF) are developed, generalizing the classical semiparametric theory. However, most existing results in this regard focus on treatment effect parameters defined in explicit forms, such as average treatment effects (ATE). In applications, economists are often confronted with tasks of inferring more complex parameters, such as quantile treatment effects (QTE) or effects of complicated treatment regimes/policy. These more complex parameters can often only be implicitly defined as the solution to nonlinear estimating equations, which correspond to M/Z-estimation problems. Our current understanding of these problems is mainly limited to the classical semiparametric theory. Given the foundational role of HOIF for estimating explicit parameters such as ATE, a modest step toward enriching the statistical foundation of econometrics and causal inference is to develop the corresponding higher-order estimators for those more complex parameters. To this end, we consider parameters of a class of non-separable structural models in the econometrics literature and develop a class of higher-order estimators for the target parameters. Statistical properties of these higher-order estimators are derived using recent advances in U-processes theory. Our proposed higher-order estimators relax complexity-reducing assumptions, quantified by Holder smoothness, imposed on the nuisance parameters compared to existing alternative estimators for many important parameters in this class, including QTE and quantile dose-response functions, among others.
appendix boundary found by appendix_command · 41% of the source is main text. Read the extracted text to check this.
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 | Nathan Kallus, Xiaojie Mao, and Masatoshi Uehara (2024) Localized debiased machine learning: Efficient inference on quantile treatment effects and beyond | 1.000 | 16 | 4 | 100% |
| 2 | Kyle Colangelo and Ying-Ying Lee (2026) Double debiased machine learning nonparametric inference with continuous treatments | 1.000 | 7 | 3 | 100% |
| 3 | James Robins, Lingling Li, Eric Tchetgen Tchetgen, and Aad van der V… (2008) Higher order influence functions and minimax estimation of nonlinear functionals | 1.000 | 6 | 3 | 100% |
| 4 | Matteo Bonvini and Edward H Kennedy (2022) Fast convergence rates for dose-response estimation | 0.965 | 10 | 4 | 90% |
| 5 | Chunrong Ai, Oliver Linton, Kaiji Motegi, and Zheng Zhang (2021) A unified framework for efficient estimation of general treatment models self | 0.946 | 13 | 6 | 85% |
| 6 | James M Robins, Lingling Li, Lin Liu, Rajarshi Mukherjee, Eric Tchet… (2023) Minimax estimation of a functional on a structured high-dimensional model (Corrected version) self | 0.941 | 6 | 4 | 83% |
| 7 | Matias D Cattaneo, Max H Farrell, Michael Jansson, and Ricardo P Mas… (2025) Higher-order refinements of small bandwidth asymptotics for density-weighted average derivative estimators | 0.928 | 5 | 4 | 80% |
| 8 | Liangjun Su, Takuya Ura, and Yichong Zhang (2019) Non-separable models with high-dimensional data self | 0.928 | 4 | 3 | 100% |
| 9 | 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 | 0.909 | 8 | 3 | 75% |
| 10 | Victor Chernozhukov, Denis Chetverikov, Mert Demirer, Esther Duflo,… (2018) Double/debiased machine learning for treatment and structural parameters | 0.874 | 5 | 2 | 100% |
Showing the top 10 of 82 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 | 1.000 | 5 | 4 |