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 (Calcutta Statist. Assoc. Bull. 33 (1984) 1–2). We show how to apply this approach to compute not only the Cramér-von-Mises indices, 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.
Funding Statement
Support from the ANR-3IA Artificial and Natural Intelligence Toulouse Institute is gratefully acknowledged. This work was also supported by the National Science Foundation under grant DMS-1745654.
Acknowledgements
We warmly thank Robin Morillo for the numerical study provided in Section 5.2. Moreover, we deeply thank the anonymous referee of the early version of our paper who pushed us to prove the CLT. We also gratefully thank the anonymous reviewer of the current version of this paper for his comments, critics and advises, which greatly helped us to improve the manuscript.
Citation
Fabrice Gamboa. Pierre Gremaud. Thierry Klein. Agnès Lagnoux. "Global sensitivity analysis: A novel generation of mighty estimators based on rank statistics." Bernoulli 28 (4) 2345 - 2374, November 2022. https://doi.org/10.3150/21-BEJ1421
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