Andrés Aradillas Fernández, José Blanchet, José Luis Montiel Olea, Chen Qiu, Jörg Stoye, Lezhi Tan
arXiv 9 Sep 2025 · Econometrics
arXiv:2509.08107 · PDF · DOI · OpenAlex · Extracted main text
A decision rule is epsilon-minimax if it is minimax up to an additive factor epsilon. We present an algorithm for provably obtaining epsilon-minimax solutions of statistical decision problems. We are interested in problems where the statistician chooses randomly among I decision rules. The minimax solution of these problems admits a convex programming representation over the (I-1)-simplex. Our suggested algorithm is a well-known mirror subgradient descent routine, designed to approximately solve the convex optimization problem that defines the minimax decision rule. This iterative routine is known in the computer science literature as the hedge algorithm and it is used in algorithmic game theory as a practical tool to find approximate solutions of two-person zero-sum games. We apply the suggested algorithm to different minimax problems in the econometrics literature. An empirical application to the problem of optimally selecting sites to maximize the external validity of an experimental policy evaluation illustrates the usefulness of the suggested procedure.
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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 | Gechter, Michael and Hirano, Keisuke and Lee, Jean and Mahmud, Mahre… (2024) Selecting Experimental Sites for External Validity | 1.000 | 8 | 3 | 100% |
| 2 | Chamberlain, Gary (2000) Econometric applications of maxmin expected utility | 1.000 | 7 | 4 | 100% |
| 3 | Ferguson, T.S (1967) Mathematical Statistics: A Decision Theoretic Approach | 1.000 | 6 | 4 | 100% |
| 4 | Bubeck, Sébastien (2015) Convex optimization: Algorithms and complexity | 0.916 | 13 | 4 | 77% |
| 5 | Stoye, Jörg (2012) Minimax regret treatment choice with covariates or with limited validity of experiments self | 0.874 | 5 | 2 | 100% |
| 6 | Arora, Sanjeev and Hazan, Elad and Kale, Satyen (2012) The multiplicative weights update method: a meta-algorithm and applications | 0.855 | 8 | 3 | 62% |
| 7 | Nemirovski, A.S. and Yudin, D.B (1983) Problem Complexity and Method Efficiency in Optimization | 0.843 | 3 | 3 | 100% |
| 8 | Ben-Tal, Aharon and Margalit, Tamar and Nemirovski, Arkadi (2001) The ordered subsets mirror descent optimization method with applications to tomography | 0.811 | 4 | 2 | 100% |
| 9 | Giacomini, Raffaella and Kitagawa, Toru (2021) Robust Bayesian inference for set-identified models | 0.811 | 4 | 2 | 100% |
| 10 | Abraham Wald (1950) Statistical Decision Functions | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 50 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
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| 1 | Statistical Decisions and Partial Identification: With Application to Boundary Discontinuity Design | 0.811 | 4 | 2 |
| 2 | Robust Bayes Treatment Choice with Partial Identification | 0.737 | 3 | 3 |