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Aggregated Intersection Bounds and Aggregated Minimax Values

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  • Vira Semenova

Abstract

This paper proposes a novel framework of aggregated intersection bounds, where the target parameter is obtained by averaging the minimum (or maximum) of a collection of regression functions over the covariate space. Examples of such quantities include the lower and upper bounds on distributional effects (Fr\'echet-Hoeffding, Makarov) as well as the optimal welfare in statistical treatment choice problems. The proposed estimator -- the envelope score estimator -- is shown to have an oracle property, where the oracle knows the identity of the minimizer for each covariate value. Next, the result is extended to the aggregated minimax values of a collection of regression functions, covering optimal distributional welfare in worst-case and best-case, respectively. This proposed estimator -- the envelope saddle value estimator -- is shown to have an oracle property, where the oracle knows the identity of the saddle point.

Suggested Citation

  • Vira Semenova, 2023. "Aggregated Intersection Bounds and Aggregated Minimax Values," Papers 2303.00982, arXiv.org, revised Jun 2024.
    • Handle: RePEc:arx:papers:2303.00982
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    2. Gyungbae Park, 2024. "Debiased Machine Learning when Nuisance Parameters Appear in Indicator Functions," Papers 2403.15934, arXiv.org.

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