A new index to measure positive dependence in trivariate distributions

JOURNAL OF MULTIVARIATE ANALYSIS

卷:115

Article

Garcia, Jesus E.¹  Gonzalez-Lopez, V. A.¹  Nelsen, R. B.² 

[1] Univ Estadual Campinas, Dept Stat, BR-13083859 Sao Paulo, Brazil

[2] Lewis & Clark Coll, Dept Math Sci, Portland, OR 97219 USA

关键词: Measure of association;    Directional dependence;    Copula;   

DOI  :  10.1016/j.jmva.2012.11.007

来源: Elsevier

【 摘 要 】

We introduce a new index to detect dependence in trivariate distributions. The index is based on the maximization of the coefficients of directional dependence over the set of directions. We show how to calculate the index using the three pairwise Spearman's rho coefficients and the three common 3-dimensional versions of Spearman's rho. We obtain the asymptotic distributions of the empirical processes related to the estimators of the coefficients of directional dependence and also we derive the asymptotic distribution of our index. We display examples where the index identifies dependence undetected by the aforementioned 3-dimensional versions of Spearman's rho. The value of the new index and the direction in which the maximal dependence occurs are easily computed and we illustrate with a simulation study and a real data set. (C) 2012 Elsevier Inc. All'rights reserved.

【 授权许可】

Free