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Article Dans Une Revue Bernoulli Année : 2022

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

Résumé

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 Cramér-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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Dates et versions

hal-02474902 , version 1 (13-02-2020)
hal-02474902 , version 2 (04-03-2020)
hal-02474902 , version 3 (06-11-2020)
hal-02474902 , version 4 (21-05-2021)
hal-02474902 , version 5 (22-02-2023)
hal-02474902 , version 6 (30-06-2023)

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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), pp.2345-2374. ⟨10.3150/21-BEJ1421⟩. ⟨hal-02474902v6⟩
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