A multivariate version of Hoeffding’s Phi-Square |
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Authors: | Sandra Gaißer Martin Ruppert Friedrich Schmid |
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Institution: | aDepartment of Economic and Social Statistics, University of Cologne, Albertus-Magnus-Platz, 50923 Köln, Germany;bGraduate School of Risk Management, University of Cologne, Albertus-Magnus-Platz, 50923 Köln, Germany |
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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. |
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Keywords: | AMS 2000 subject class: Primary 62H20 60F05 62G20 Secondary 60G15 62G10 |
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