Large-sample tests of extreme-value dependence for multivariate copulas

Ivan Kojadinovic (1) , J. Segers (2) , J. Yan (3)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 Institut de Statistique, Biostatistique et Sciences Actuarielles (ISBA)
3 Center for Human Genetics, University of Leuven School of Medicine

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. © 2011 Statistical Society of Canada.

Domaines: Probabilités [math.PR]

Ivan Kojadinovic, J. Segers, J. Yan. Large-sample tests of extreme-value dependence for multivariate copulas. Canadian Journal of Statistics, 2011, 39 (4), pp.703-720. ⟨10.1002/cjs.10110⟩. ⟨hal-00865055⟩