Title: Multivariate Dependency Measure based on Copula and Gaussian Kernel,
Abstract: 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.