A multivariate version of Hoeffding's Phi-Square

JOURNAL OF MULTIVARIATE ANALYSIS

卷:101

Article

Gaisser, Sandra²  Ruppert, Martin¹  Schmid, Friedrich² 

[1] Univ Cologne, Grad Sch Risk Management, D-50923 Cologne, Germany

[2] Univ Cologne, Dept Econ & Social Stat, D-50923 Cologne, Germany

关键词: Multivariate measure of association;    Copula;    Nonparametric estimation;    Empirical copula process;    Weak convergence;    Nonparametric bootstrap;    Strong mixing;   

DOI  :  10.1016/j.jmva.2010.07.006

来源: Elsevier

【 摘 要 】

A multivariate measure of association is proposed, which extends the bivariate copula-based measure Phi-Square introduced by Hoeffding [22]. We discuss its analytical properties and calculate its explicit value for some copulas of simple form; a simulation procedure to approximate its value is provided otherwise. A nonparametric estimator for multivariate Phi-Square is derived and its asymptotic behavior is established based on the weak convergence of the empirical copula process both in the case of independent observations and dependent observations from strictly stationary strong mixing sequences. The asymptotic variance of the estimator can be estimated by means of nonparametric bootstrap methods. For illustration, the theoretical results are applied to financial asset return data. (c) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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