On rank correlation measures for non-continuous random variables

Authors:
Johanna Nešlehová
Affiliations:
RiskLab, Department of Mathematics, ETH Zurich, CH-8092 Zurich, Switzerland
Venue:
Journal of Multivariate Analysis
Year:
2007

Citing 2
Cited 3

Constraints on concordance measures in bivariate discrete data

Journal of Multivariate Analysis
An Introduction to Copulas (Springer Series in Statistics)

An Introduction to Copulas (Springer Series in Statistics)

Concordance measures for multivariate non-continuous random vectors

Journal of Multivariate Analysis
A Simulation-Based Approach to Decision Making with Partial Information

Decision Analysis
On the estimation of Spearman's rho and related tests of independence for possibly discontinuous multivariate data

Journal of Multivariate Analysis

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Abstract

For continuous random variables, many dependence concepts and measures of association can be expressed in terms of the corresponding copula only and are thus independent of the marginal distributions. This interrelationship generally fails as soon as there are discontinuities in the marginal distribution functions. In this paper, we consider an alternative transformation of an arbitrary random variable to a uniformly distributed one. Using this technique, the class of all possible copulas in the general case is investigated. In particular, we show that one of its members-the standard extension copula introduced by Schweizer and Sklar-captures the dependence structures in an analogous way the unique copula does in the continuous case. Furthermore, we consider measures of concordance between arbitrary random variables and obtain generalizations of Kendall's tau and Spearman's rho that correspond to the sample version of these quantities for empirical distributions.