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Global sensitivity analysis: A novel generation of mighty estimators based on rank statistics

Fabrice Gamboa Pierre Gremaud Thierry Klein 1 Agnès Lagnoux 
1 DEVI - Données, Economie et Visualisation
ENAC - Ecole Nationale de l'Aviation Civile
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
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https://hal-enac.archives-ouvertes.fr/hal-03827435
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Soumis le : lundi 24 octobre 2022 - 16:16:43
Dernière modification le : mardi 25 octobre 2022 - 03:16:14

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Fabrice Gamboa, Pierre Gremaud, Thierry Klein, Agnès Lagnoux. Global sensitivity analysis: A novel generation of mighty estimators based on rank statistics. Bernoulli, 2022, 28 (4), ⟨10.3150/21-BEJ1421⟩. ⟨hal-03827435⟩

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