Symmetric rank covariances: a generalized framework for nonparametric measures of dependence
对称秩协方差：非参数依赖度量的广义框架
The need to test whether two random vectors are independent has spawned many competing measures of dependence. We focus on nonparametric measures that are invariant under strictly increasing transformations, such as Kendall’s tau, Hoeffding’s |$D$|, and the Bergsma–Dassios sign covariance. Each exhibits symmetries that are not readily apparent from their definitions. Making these symmetries explicit, we define a new class of multivariate nonparametric measures of dependence…