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BY 4.0 license Open Access Published by De Gruyter Open Access July 5, 2021

Study of partial and average conditional Kendall’s tau

Irène Gijbels and Margot Matterne
From the journal Dependence Modeling

Abstract

When the interest is in studying conditional dependencies, and more precisely the strength of conditional dependencies, some kind of averaging over the conditioning random vector may be needed. Examples of average measures that can serve in this context are the average conditional Kendall’s tau and partial Kendall’s tau. It is known that these measures differ in general. Some statistical tests are based on these average measures, and a better knowledge of them is of importance. The aim of this paper is to provide a quantitative study of the possible differences of these two average measures, and to establish su˚cient conditions under which they coincide. Both measures are studied in two fairly general settings. In each setting theoretical results are established as well as several illustrative examples given.

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Received: 2020-06-22
Accepted: 2021-05-17
Published Online: 2021-07-05

© 2021 Irène Gijbels et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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