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Epsilon-Minimax Solutions of Statistical Decision Problems

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

Abstract

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.

Citation extraction

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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Gechter, Michael and Hirano, Keisuke and Lee, Jean and Mahmud, Mahre… (2024) Selecting Experimental Sites for External Validity1.00083100%
2Chamberlain, Gary (2000) Econometric applications of maxmin expected utility1.00074100%
3Ferguson, T.S (1967) Mathematical Statistics: A Decision Theoretic Approach1.00064100%
4Bubeck, Sébastien (2015) Convex optimization: Algorithms and complexity0.91613477%
5Stoye, Jörg (2012) Minimax regret treatment choice with covariates or with limited validity of experiments self0.87452100%
6Arora, Sanjeev and Hazan, Elad and Kale, Satyen (2012) The multiplicative weights update method: a meta-algorithm and applications0.8558362%
7Nemirovski, A.S. and Yudin, D.B (1983) Problem Complexity and Method Efficiency in Optimization0.84333100%
8Ben-Tal, Aharon and Margalit, Tamar and Nemirovski, Arkadi (2001) The ordered subsets mirror descent optimization method with applications to tomography0.81142100%
9Giacomini, Raffaella and Kitagawa, Toru (2021) Robust Bayesian inference for set-identified models0.81142100%
10Abraham Wald (1950) Statistical Decision Functions0.73732100%

Showing the top 10 of 50 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Statistical Decisions and Partial Identification: With Application to Boundary Discontinuity Design0.81142
2Robust Bayes Treatment Choice with Partial Identification0.73733