A nonparametric test of serial independence for time series and residuals
Journal of Multivariate Analysis
Constraints on concordance measures in bivariate discrete data
Journal of Multivariate Analysis
On rank correlation measures for non-continuous random variables
Journal of Multivariate Analysis
Concordance measures for multivariate non-continuous random vectors
Journal of Multivariate Analysis
An Introduction to Copulas
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Tie-corrected versions of Spearman's rho are often used to measure the dependence in a pair of non-continuous random variables. Multivariate extensions of this coefficient, and estimators thereof, have recently been proposed by Quessy (2009a) [23] and Mesfioui and Quessy (2010) [19]. Asymptotically equivalent but numerically much simpler estimators of the same coefficients are given here. Expressions are also provided for their limiting variance, thereby correcting errors in these authors' papers. It is further shown that the Mobius decomposition of the multilinear extension (or checkerboard) copula leads to tie-corrected versions of dependence coefficients originally introduced by Genest and Remillard (2004) [10]. These coefficients can be used to visualize dependence structures and to construct tests of mutual independence that can be more powerful than those based on tie-corrected versions of Spearman's rho.