English

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

Methodology 2026-05-25 v1

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.

Cite

@article{arxiv.2605.23760,
  title  = {Global Sensitivity Analysis: a novel generation of mighty estimators based on rank statistics},
  author = {Fabrice Gamboa and Pierre Gremaud and Thierry Klein and Agnès Lagnoux},
  journal= {arXiv preprint arXiv:2605.23760},
  year   = {2026}
}

Comments

Erratum for Global Sensitivity Analysis: a novel generation of mighty estimators based on rank statistics. Fabrice Gamboa, Thierry Klein, Agn{\`e}s Lagnoux, and Paul Rochet. arXiv admin note: substantial text overlap with arXiv:2003.01772