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

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

Mots clés: Chatterjee’s coefficient of correlation; Cramér-von-Mises distance; Global sensitivity analysis; Pick-Freeze method; Sobol’ indices estimation

Domaines: Mathématiques [math]

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⟩