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.

翻译：我们提出了一种适用于大类全局敏感性分析方法的新统计估计框架。该方法基于秩统计，利用Sourav Chatterjee近期引入的经验相关系数。我们展示了如何应用这一框架不仅计算与Chatterjee相关性概念直接相关的克拉默-冯·米塞斯指数，还可计算任意阶次的索博尔指数、高阶矩指数以及沙普利效应。我们证明了所得估计量的一致性，并展示了其数值效率，尤其在样本量较小时表现突出。