Yikun Zhang, Yen-Chi Chen
arXiv 12 Jan 2025 · Statistics — Methodology
arXiv:2501.06969 · PDF · Extracted main text
Statistical methods for causal inference with continuous treatments mainly focus on estimating the mean potential outcome function, commonly known as the dose-response curve. However, it is often not the dose-response curve but its derivative function that signals the treatment effect. In this paper, we investigate nonparametric inference on the derivative of the dose-response curve with and without the positivity condition. Under the positivity and other regularity conditions, we propose a doubly robust (DR) inference method for estimating the derivative of the dose-response curve using kernel smoothing. When the positivity condition is violated, we demonstrate the inconsistency of conventional inverse probability weighting (IPW) and DR estimators, and introduce novel bias-corrected IPW and DR estimators. In all settings, our DR estimator achieves asymptotic normality at the standard nonparametric rate of convergence with nonparametric efficiency guarantees. Additionally, our approach reveals an interesting connection to nonparametric support and level set estimation problems. Finally, we demonstrate the applicability of our proposed estimators through simulations and a case study of evaluating a job training program.
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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 | Y. Zhang, Y.-C. Chen, and A. Giessing (2024) Nonparametric inference on dose-response curves without the positivity condition | 1.000 | 5 | 4 | 100% |
| 2 | E. H. Kennedy, Z. Ma, M. D. McHugh, and D. S. Small (2017) Nonparametric methods for doubly robust estimation of continuous treatment effects | 1.000 | 5 | 3 | 100% |
| 3 | M. Huber, Y.-C. Hsu, Y.-Y. Lee, and L. Lettry (2020) Direct and indirect effects of continuous treatments based on generalized propensity score weighting | 0.928 | 4 | 3 | 100% |
| 4 | S. Klosin (2021) Automatic double machine learning for continuous treatment effects | 0.855 | 8 | 5 | 62% |
| 5 | K. Takatsu and T. Westling (2025) Debiased inference for a covariate-adjusted regression function | 0.843 | 3 | 3 | 100% |
| 6 | K. Colangelo and Y.-Y. Lee (2020) Double debiased machine learning nonparametric inference with continuous treatments | 0.840 | 32 | 8 | 59% |
| 7 | A. Cuevas and R. Fraiman (1997) A plug-in approach to support estimation | 0.737 | 3 | 2 | 100% |
| 8 | Y. Mack and H.-G. Müller (1989) Derivative estimation in nonparametric regression with random predictor variable | 0.737 | 3 | 2 | 100% |
| 9 | L. Wasserman (2006) All of nonparametric statistics | 0.737 | 3 | 2 | 100% |
| 10 | I. Dáz and M. J. van der Laan (2013) Targeted data adaptive estimation of the causal dose–response curve | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 98 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Heterogeneous Responses to Continuous Treatments: A Cluster-Based Causal Framework | 0.405 | 1 | 1 |
| 2 | Unifying regression-based and design-based causal inference in time-series experiments | 0.405 | 1 | 1 |