  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
Cram\'er-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.
