Yizhen Xu, Numair Sani, AmirEmad Ghassami, Ilya Shpitser
arXiv 19 May 2021 · Mathematics — Statistics Theory · 1 citations (OpenAlex)
arXiv:2105.09254 · PDF · DOI · OpenAlex · Extracted main text
In many applications, researchers are interested in the direct and indirect causal effects of a treatment or exposure on an outcome of interest. Mediation analysis offers a rigorous framework for identifying and estimating these causal effects. For binary treatments, efficient estimators for the direct and indirect effects are presented by Tchetgen Tchetgen and Shpitser (2012) based on the influence function of the parameter of interest. These estimators possess desirable properties such as multiple-robustness and asymptotic normality while allowing for slower than root-n rates of convergence for the nuisance parameters. However, in settings involving continuous treatments, these influence function-based estimators are not readily applicable without making strong parametric assumptions. In this work, utilizing a kernel-smoothing approach, we propose an estimator suitable for settings with continuous treatments inspired by the influence function-based estimator of Tchetgen Tchetgen and Shpitser (2012). Our proposed approach employs cross-fitting, relaxing the smoothness requirements on the nuisance functions and allowing them to be estimated at slower rates than the target parameter. Additionally, similar to influence function-based estimators, our proposed estimator is multiply robust and asymptotically normal, allowing for inference in settings where parametric assumptions may not be justified.
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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 | Huber, M., Hsu, Y.-C., Lee, Y.-Y., and Lettry, L (2020) Direct and indirect effects of continuous treatments based on generalized propensity score weighting | 1.000 | 9 | 3 | 100% |
| 2 | Tchetgen Tchetgen, E. and Shpitser, I (2012) Semiparametric theory for causal mediation analysis: efficiency bounds, multiple robustness, and sensitivity analysis self | 1.000 | 8 | 4 | 100% |
| 3 | Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C… (2018) Double/debiased machine learning for treatment and structural parameters | 0.928 | 4 | 4 | 100% |
| 4 | Bickel, P. J., Klaassen, C. A., Bickel, P. J., Ritov, Y., Klaassen,… (1993) Efficient and adaptive estimation for semiparametric models, volume 4 | 0.843 | 3 | 3 | 100% |
| 5 | Silverman, B. W (2018) Density estimation for statistics and data analysis | 0.843 | 3 | 3 | 100% |
| 6 | Tsiatis, A (2007) Semiparametric theory and missing data | 0.843 | 3 | 3 | 100% |
| 7 | Pearl, J (2001) Direct and indirect effects | 0.811 | 4 | 2 | 100% |
| 8 | Colangelo, K. and Lee, Y.-Y (2020) Double debiased machine learning nonparametric inference with continuous treatments | 0.737 | 3 | 2 | 100% |
| 9 | Imai, K., Keele, L., and Yamamoto, T (2010) Identification, inference and sensitivity analysis for causal mediation effects | 0.737 | 3 | 2 | 100% |
| 10 | Kennedy, E. H., Ma, Z., McHugh, M. D., and Small, D. S (2017) Nonparametric methods for doubly robust estimation of continuous treatment effects | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 39 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Sequential kernel embedding for mediated and time-varying dose response curves | 0.405 | 1 | 1 |