AUK-based test for mutual independence and an index of mutual dependence

We offer a novel test of mutual independence based on consistent estimates of the area under the Kendall curve. We also present an index of dependence that allows one to measure the mutual dependence of a d-dimensional random vector with d>2. The index is based on a d-dimensional Kendall process. We discuss a standardized version of our index of dependence that is easy to interpret, and provide an algorithm for its computation. Based on the proposed index of dependence, we exemplify a novel method for searching for patterns in the dependence structure. We evaluate the performance of our procedures via simulation, and apply our methods to a real data set.