Yanqin Fan, Hyeonseok Park, Gaoqian Xu
arXiv 3 Jul 2023 · Mathematics — Optimization · publishedMathematics of Operations Research (2025) · 3 citations (OpenAlex)
arXiv:2307.00779 · PDF · DOI · OpenAlex · Extracted main text
This paper studies distributional model risk in marginal problems, where each marginal measure is assumed to lie in a Wasserstein ball centered at a fixed reference measure with a given radius. Theoretically, we establish several fundamental results including strong duality, finiteness of the proposed Wasserstein distributional model risk, and the existence of an optimizer at each radius. In addition, we show continuity of the Wasserstein distributional model risk as a function of the radius. Using strong duality, we extend the well-known Makarov bounds for the distribution function of the sum of two random variables with given marginals to Wasserstein distributionally robust Markarov bounds. Practically, we illustrate our results on four distinct applications when the sample information comes from multiple data sources and only some marginal reference measures are identified. They are: partial identification of treatment effects; externally valid treatment choice via robust welfare functions; Wasserstein distributionally robust estimation under data combination; and evaluation of the worst aggregate risk measures.
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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 | Blanchet, Jose, Murthy, Karthyek (2019) Quantifying Distributional Model Risk via Optimal Transport | 1.000 | 8 | 3 | 100% |
| 2 | Rüschendorf, Ludger (1991) Bounds for distributions with multivariate marginals | 1.000 | 8 | 3 | 100% |
| 3 | Embrechts, Paul, Puccetti, Giovanni (2010) Bounds for the sum of dependent risks having overlapping marginals | 1.000 | 6 | 3 | 100% |
| 4 | Awasthi, Pranjal, Jung, Christopher, Morgenstern, Jamie (2022) Distributionally Robust Data Join | 1.000 | 6 | 3 | 100% |
| 5 | Fan, Yanqin, Guerre, Emmanuel, Zhu, Dongming (2017) Partial identification of functionals of the joint distribution of “potential outcomes” self | 1.000 | 5 | 4 | 100% |
| 6 | Adjaho, Christopher, Christensen, Timothy (2023) Externally Valid Policy Choice | 0.946 | 13 | 4 | 85% |
| 7 | Villani, Cédric (2021) Topics in optimal transportation | 0.928 | 5 | 4 | 80% |
| 8 | Fan, Yanqin, Wu, Jisong (2009) Partial identification of the distribution of treatment effects in switching regime models and its confidence sets self | 0.928 | 4 | 3 | 100% |
| 9 | Zhang, Luhao, Yang, Jincheng, Gao, Rui (2022) A simple duality proof for wasserstein distributionally robust optimization | 0.923 | 14 | 6 | 79% |
| 10 | Villani, Cédric (2009) Optimal transport: old and new | 0.894 | 7 | 5 | 71% |
Showing the top 10 of 60 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | An econometrician's guide to optimal transport | 0.644 | 4 | 1 |
| 2 | Distributionally Robust Instrumental Variables Estimation | 0.511 | 2 | 2 |
| 3 | Policy Learning with $$-Expected Welfare | 0.405 | 1 | 1 |
| 4 | Distributionally Robust Treatment Effect | 0.405 | 1 | 1 |