论文标题
全球灵敏度分析：基于等级统计的新一代强大估计器
Global Sensitivity Analysis: a new generation of mighty estimators based on rank statistics
论文作者
论文摘要
我们为大型全球灵敏度分析方法提供了一个新的统计估计框架。我们的方法基于等级统计，并使用Sourav Chatterjee最近引入的经验相关系数。我们展示了如何应用这种方法来计算Cramér-von-Mises指数，这些指数与Chatterjee的相关性概念直接相关，而且在任何顺序，高阶时刻索引和Shapley效果下也是SOBOL指数。我们建立了由此产生的估计器的一致性，并证明了它们的数值效率，尤其是对于小样本量。
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 Cramér-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.
