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

By Fabrice Gamboa, Pierre-Alain Gremaud, Thierry Klein, Agnès Lagnoux. 2020

53 citations recorded by the source corpus.

We propose a new statistical estimation framework for a large family of global sensitivity analysis methods. Our approach is based on rank statistics and uses an empirical correlation coefficient recently introduced by Sourav Chatterjee. We show how to apply this approach to compute not only the Cramer-von-Mises indices, which are directly related to Chatterjee's notion of correlation, but also Sobol indices at any order, higher-order moment indices, and Shapley effects. We establish consistency of the resulting estimators and demonstrate their numerical efficiency, especially for small sample sizes.

Subfields: Computational Theory and Mathematics, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5ba708416a5ecd65953ffff061f20cd4133f5706

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Hongjian Shi
2. Mathias Drton
3. Fang Han
4. Bernd Sturmfels

In Statistical and Nonlinear Physics

1. Hongjian Shi
2. Mathias Drton
3. Fang Han

In Statistics and Probability

1. Fang Han
2. Hongjian Shi
3. Mathias Drton
4. Marloes H. Maathuis
5. Sacha Epskamp
6. Bodhisattva Sen
7. Nabarun Deb
8. Zhexiao Lin

Citations in the corpus

• On Azadkia–Chatterjee’s conditional dependence coefficient (2021, background): “where the last step applies bounds on the expectation of the maximum of random variables (see Gilstein (1981) or Arnold (1985, Theorem 3)) to Assumption 4.”