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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2511.04457 |
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| _version_ | 1866911251729219584 |
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| author | Gonzalez-Hodar, Jaime Milz, Johannes Song, Eunhye |
| author_facet | Gonzalez-Hodar, Jaime Milz, Johannes Song, Eunhye |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04457 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonparametric Robust Comparison of Solutions under Input Uncertainty Gonzalez-Hodar, Jaime Milz, Johannes Song, Eunhye Methodology 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. |
| title | Nonparametric Robust Comparison of Solutions under Input Uncertainty |
| topic | Methodology |
| url | https://arxiv.org/abs/2511.04457 |