Large‐sample tests of extreme‐value dependence for multivariate copulas |
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| Authors: | Ivan Kojadinovic Johan Segers Jun Yan |
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| Institution: | 1. Laboratoire de Mathématiques et Applications, UMR CNRS 5142, Université de Pau et des Pays de l'Adour, BP 1155, 64013 Pau Cedex, France;2. Institut de statistique, biostatistique et sciences actuarielles, Université catholique de Louvain, Voie du Roman Pays 20, B‐1348 Louvain‐la‐Neuve, Belgium;3. Department of Statistics, University of Connecticut, 215 Glenbrook Rd. U‐4120, Storrs, CT 06269, USA |
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| Abstract: | Starting from the characterization of extreme‐value copulas based on max‐stability, large‐sample tests of extreme‐value dependence for multivariate copulas are studied. The two key ingredients of the proposed tests are the empirical copula of the data and a multiplier technique for obtaining approximate p‐values for the derived statistics. The asymptotic validity of the multiplier approach is established, and the finite‐sample performance of a large number of candidate test statistics is studied through extensive Monte Carlo experiments for data sets of dimension two to five. In the bivariate case, the rejection rates of the best versions of the tests are compared with those of the test of Ghoudi et al. (1998) recently revisited by Ben Ghorbal et al. (2009). The proposed procedures are illustrated on bivariate financial data and trivariate geological data. The Canadian Journal of Statistics 39: 703–720; 2011. © 2011 Statistical Society of Canada |
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| Keywords: | Max‐stability multiplier central limit theorem pseudo‐observations ranks 62H15 62G32 62G09 62G30 |
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