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

JOURNAL OF MULTIVARIATE ANALYSIS

卷:117

Article

Genest, Christian¹  Neslehova, Johanna G.¹  Remillard, Bruno² 

[1] McGill Univ, Dept Math & Stat, Montreal, PQ H3A 0B9, Canada

[2] HEC Montreal, Serv Enseignement Methodes Quantitat Gest, Montreal, PQ H3T 2A7, Canada

关键词: Asymptotic variance;    Checkerboard copula;    Dependogram;    Multilinear extension copula;    Rank-based inference;    Spearman's rho;    Ties;    U-statistic;   

DOI  :  10.1016/j.jmva.2013.02.007

来源: Elsevier

【 摘 要 】

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. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free