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

Georgios Afendras; Marianthi Markatou; Albert Vexler

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arXiv · 2011.12268

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

Georgios Afendras·Marianthi Markatou·Albert Vexler

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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.

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Georgios Afendras, Marianthi Markatou, Albert Vexler. 2020-11-24. An AUK-based index for measuring and testing the joint dependence of a random vector. https://arxiv.org/abs/2011.12268

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