Multivariate Dependency Measure based on Copula and Gaussian Kernel
This provides a new statistical tool for measuring dependencies in multivariate data, though it appears incremental relative to existing copula-based approaches.
The authors proposed a new multivariate dependency measure based on copula transforms and Gaussian kernels, which satisfies desirable properties and includes a nonparametric estimator and independence test. They demonstrated competitive performance against existing methods on artificial datasets.
We propose a new multivariate dependency measure. It is obtained by considering a Gaussian kernel based distance between the copula transform of the given d-dimensional distribution and the uniform copula and then appropriately normalizing it. The resulting measure is shown to satisfy a number of desirable properties. A nonparametric estimate is proposed for this dependency measure and its properties (finite sample as well as asymptotic) are derived. Some comparative studies of the proposed dependency measure estimate with some widely used dependency measure estimates on artificial datasets are included. A non-parametric test of independence between two or more random variables based on this measure is proposed. A comparison of the proposed test with some existing nonparametric multivariate test for independence is presented.