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

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 Cram??r-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.

Automated summary

In this paper, we propose a new statistical estimation framework for calculating various global sensitivity analysis indices. We demonstrate the effectiveness and numerical efficiency of our method and establish the consistency of the resulting estimators.