Multivariate Dependency Measure based on Copula and Gaussian Kernel

TL;DR

This paper introduces a novel multivariate dependency measure using copula transforms and Gaussian kernels, along with a nonparametric independence test, demonstrating favorable properties and performance through comparative studies.

Contribution

It presents a new dependency measure based on copula and Gaussian kernels, including a nonparametric estimation method and an independence test, with theoretical and empirical validation.

Findings

The measure satisfies desirable properties.

The nonparametric estimate performs well on artificial data.

The independence test compares favorably with existing methods.

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.