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A multivariate version of Hoeffding's Phi-Square

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  • Gaißer, Sandra
  • Ruppert, Martin
  • Schmid, Friedrich

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.

Suggested Citation

  • Gaißer, Sandra & Ruppert, Martin & Schmid, Friedrich, 2010. "A multivariate version of Hoeffding's Phi-Square," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2571-2586, November.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:10:p:2571-2586
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    References listed on IDEAS

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    2. De Keyser, Steven & Gijbels, Irène, 2024. "Parametric dependence between random vectors via copula-based divergence measures," Journal of Multivariate Analysis, Elsevier, vol. 203(C).
    3. Jafar Rahmanishamsi & Ali Dolati & Masoudreza R. Aghabozorgi, 2018. "A Copula Based ICA Algorithm and Its Application to Time Series Clustering," Journal of Classification, Springer;The Classification Society, vol. 35(2), pages 230-249, July.
    4. Stavrakoudis, Athanassios & Panagiotou, Dimitrios, 2016. "Price dependence between coffee qualities: a copula model to evaluate asymmetric responses," MPRA Paper 75994, University Library of Munich, Germany.
    5. García, Jesús E. & González-López, V.A. & Nelsen, R.B., 2013. "A new index to measure positive dependence in trivariate distributions," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 481-495.
    6. Liebscher Eckhard, 2014. "Copula-based dependence measures," Dependence Modeling, De Gruyter, vol. 2(1), pages 1-16, October.
    7. Stavrakoudis, Athanassios & Panagiotou, Dimitrios, 2016. "Price dependence and asymmetric responses between coffee varieties," Agricultural Economics Review, Greek Association of Agricultural Economists, vol. 17(2), June.
    8. Panagiotou Dimitrios & Stavrakoudis Athanassios, 2016. "Price Dependence between Different Beef Cuts and Quality Grades: A Copula Approach at the Retail Level for the U.S. Beef Industry," Journal of Agricultural & Food Industrial Organization, De Gruyter, vol. 14(1), pages 121-131, May.
    9. Panagiotou, Dimitrios & Stavrakoudis, Athanassios, 2017. "Vertical price relationships between different cuts and quality grades in the U.S. beef marketing channel: A wholesale-retail analysis," The Journal of Economic Asymmetries, Elsevier, vol. 16(C), pages 53-63.
    10. Angshuman Roy & Anil K. Ghosh & Alok Goswami & C. A. Murthy, 2022. "Some New Copula Based Distribution-free Tests of Independence among Several Random Variables," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 556-596, August.
    11. Dehghan, Sakineh & Faridrohani, Mohammad Reza, 2024. "A data depth based nonparametric test of independence between two random vectors," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    12. Patton, Andrew J., 2012. "A review of copula models for economic time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 4-18.
    13. Patton, Andrew, 2013. "Copula Methods for Forecasting Multivariate Time Series," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 899-960, Elsevier.

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