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

2026-05-22

AI Summary

This study addresses the inefficiency and instability of traditional global sensitivity analysis methods under small sample sizes. The authors propose a unified nonparametric estimation framework based on rank statistics and Chatterjee’s recently introduced empirical correlation coefficient, extending it for the first time to diverse sensitivity indices—including Cramér–von Mises, first-order Sobol’, metric space–based measures, and higher-order moments. Theoretical analysis establishes the consistency and asymptotic normality of the proposed estimators. Numerical experiments demonstrate that the method achieves superior computational efficiency and stability in small-sample settings, offering a theoretically grounded and practically effective new tool for global sensitivity analysis.

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 [9]. We show how to apply this approach to compute not only the Cram{é}r-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.

Problem

• Global Sensitivity Analysis
• Sobol indices
• rank statistics
• Cramér-von-Mises indices
• statistical estimation

Innovation

• rank statistics
• global sensitivity analysis
• Chatterjee correlation
• Sobol indices
• empirical estimation