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Gaisser, Sandra, Ruppert, Martin and Schmid, Friedrich (2010). A multivariate version of Hoeffding's Phi-Square. J. Multivar. Anal., 101 (10). S. 2571 - 2587. SAN DIEGO: ELSEVIER INC. ISSN 0047-259X

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Abstract

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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Gaisser, Sandra UNSPECIFIED UNSPECIFIED UNSPECIFIED Ruppert, Martin UNSPECIFIED UNSPECIFIED UNSPECIFIED Schmid, Friedrich UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-493600
DOI:	10.1016/j.jmva.2010.07.006
Journal or Publication Title:	J. Multivar. Anal.
Volume:	101
Number:	10
Page Range:	S. 2571 - 2587
Date:	2010
Publisher:	ELSEVIER INC
Place of Publication:	SAN DIEGO
ISSN:	0047-259X
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language ACTUARIAL SCIENCE; RANDOM-VARIABLES; TAIL DEPENDENCE; BLOMQVISTS-BETA; SPEARMANS-RHO; INDEPENDENCE; COMONOTONICITY; ASSOCIATION; CONCORDANCE; STATISTICS Multiple languages Statistics & Probability Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/49360