Global Sensitivity Analysis: a novel generation of mighty estimators based on rank statistics
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914592620281856 |
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| author | Gamboa, Fabrice Gremaud, Pierre Klein, Thierry Lagnoux, Agnès |
| author_facet | Gamboa, Fabrice Gremaud, Pierre Klein, Thierry Lagnoux, Agnès |
| contents | We propose a new statistical estimation framework for a large family of global sensitivity analysis indices. Our approach is based on rank statistics and uses an empirical correlation coefficient recently introduced by Chatterjee [9]. We show how to apply this approach to compute not only the Cram{é}r-von-Mises indices, which are directly related to Chatterjee's notion of correlation, but also first-order Sobol indices, general metric space indices and higher-order moment indices. We establish consistency of the resulting estimators and demonstrate their numerical efficiency, especially for small sample sizes. In addition, we prove a central limit theorem for the estimators of the first-order Sobol indices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_23760 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global Sensitivity Analysis: a novel generation of mighty estimators based on rank statistics Gamboa, Fabrice Gremaud, Pierre Klein, Thierry Lagnoux, Agnès Methodology We propose a new statistical estimation framework for a large family of global sensitivity analysis indices. Our approach is based on rank statistics and uses an empirical correlation coefficient recently introduced by Chatterjee [9]. We show how to apply this approach to compute not only the Cram{é}r-von-Mises indices, which are directly related to Chatterjee's notion of correlation, but also first-order Sobol indices, general metric space indices and higher-order moment indices. We establish consistency of the resulting estimators and demonstrate their numerical efficiency, especially for small sample sizes. In addition, we prove a central limit theorem for the estimators of the first-order Sobol indices. |
| title | Global Sensitivity Analysis: a novel generation of mighty estimators based on rank statistics |
| topic | Methodology |
| url | https://arxiv.org/abs/2605.23760 |