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arXiv · 2605.23760

Global Sensitivity Analysis: a novel generation of mighty estimators based on rank statistics

Fabrice Gamboa·Pierre Gremaud·Thierry Klein·Agnès Lagnoux
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Abstract

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{\'e}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.

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Fabrice Gamboa, Pierre Gremaud, Thierry Klein, Agnès Lagnoux. 2026-05-22. Global Sensitivity Analysis: a novel generation of mighty estimators based on rank statistics. https://arxiv.org/abs/2605.23760

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