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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.04457 |
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Table of Contents:
- We study ranking and selection under input uncertainty in settings where additional data cannot be collected. We propose the Nonparametric Input-Output Uncertainty Comparisons (NIOU-C) procedure to construct a confidence set that includes the optimal solution with a user-specified probability. We construct an ambiguity set of input distributions using empirical likelihood and approximate the mean performance of each solution using a linear functional representation of the input distributions. By solving optimization problems evaluating worst-case pairwise mean differences within the ambiguity set, we build a confidence set of solutions indistinguishable from the optimum. We characterize sample size requirements for NIOU-C to achieve the asymptotic validity under mild conditions. Moreover, we propose an extension to NIOU-C, NIOU-C:E, that mitigates conservatism and yields a smaller confidence set. In numerical experiments, NIOU-C provides a smaller confidence set that includes the optimum more frequently than a parametric procedure that takes advantage of the parametric distribution families.