An AUK-based index for measuring and testing the joint dependence of a random vector

TL;DR

This paper introduces a new dependence index for multivariate data based on a d-dimensional Kendall process, along with standardized versions, algorithms, and tests for total independence, validated through simulations and real data applications.

Contribution

It proposes a novel joint dependence index for high-dimensional vectors, with standardized form, computational algorithm, and independence testing methods.

Findings

The index effectively measures joint dependence in multivariate data.

The standardized index is easy to interpret and compute.

Simulation studies demonstrate the method's good performance.

Abstract

We present an index of dependence that allows one to measure the joint or mutual dependence of a $d$-dimensional random vector with $d>2$. The index is based on a $d$-dimensional Kendall process. We further propose a standardized version of our index of dependence that is easy to interpret, and provide an algorithm for its computation. We discuss tests of total independence based on consistent estimates of the area under the Kendall curve. We evaluate the performance of our procedures via simulation, and apply our methods to a real data set.