In this paper, we introduce new indices adapted to outputs valued in general metric spaces. This new class of indices encompasses the classical ones; in particular, the so-called Sobol indices and the Cram{\'e}r-von-Mises indices. Furthermore, we provide asymptotically Gaussian estimators of these indices based on U-statistics. Surprisingly, we prove the asymp-totic normality straightforwardly. Finally, we illustrate this new procedure on a toy model and on two real-data examples.
Cite
@article{arxiv.2002.04465,
title = {Sensitivity analysis in general metric spaces},
author = {Fabrice Gamboa and Thierry Klein and Agnès Lagnoux and Leonardo Moreno},
journal= {arXiv preprint arXiv:2002.04465},
year = {2021}
}