Working with so-called linkages allows to define a copula-based, -valued multivariate dependence measure quantifying the scale-invariant extent of dependence of a random variable Y on a d-dimensional random vector which exhibits various good and natural properties. In particular, if and only if X and Y are independent, is maximal exclusively if Y is a function of X, and ignoring one or several coordinates of X can not increase the resulting dependence value. After introducing and analyzing the metric underlying the construction of the dependence measure and deriving examples showing how much information can be lost by only considering all pairwise dependence values we derive a so-called checkerboard estimator for and show that it is strongly consistent in full generality, i.e., without any smoothness restrictions on the underlying copula. Some simulations illustrating the small sample performance of the estimator complement the established theoretical results.
The first and the second author gratefully acknowledge the support of the Austrian FWF START project Y1102 ‘Successional Generation of Functional Multidiversity’. Moreover, the third author gratefully acknowledges the support of the WISS 2025 project ‘IDA-lab Salzburg’ (20204-WISS/225/197-2019 and 0102-F1901166-KZP).
Florian Griessenberger. Robert R. Junker. Wolfgang Trutschnig. "On a multivariate copula-based dependence measure and its estimation." Electron. J. Statist. 16 (1) 2206 - 2251, 2022. https://doi.org/10.1214/22-EJS2005