Pseudo‐likelihood ratio tests for semiparametric multivariate copula model selection

The authors propose pseudo-likelihood ratio tests for selecting semiparametric multivariate copula models in which the marginal distributions are unspecified, but the copula function is parameterized and can be misspecified. For the comparison of two models, the tests differ depending on whether the two copulas are generalized nonnested or generalized nested. For more than two models, the procedure is built on the reality check test of White (2000). Unlike White (2000), however, the test statistic is automatically standardized for generalized nonnested models (with the benchmark) and ignores generalized nested models asymptotically. The authors illustrate their approach with American insurance claim data. Tests du rapport des pseudo-vraisemblances pour la selection de modeles de copules multivaries semiparametriques: Les auteurs proposent l'emploi de tests du rapport des pseudo-vraisemblances pour la selection de modeles de copules multivaries semiparametriques dans lesquels les marges ne sont pas precisees et la copule parametrique peut eventuellement ětre ma1 specifiee. La forme du test permettant de comparer deux modeles varie selon que les copules sous-jacentes sont emboitees ou non dans un sens large. La procedure permettant de comparer plusieurs modeles a la fois s'inspire du test de realisme de White (2000). A la difference de ce demier, cependant, la statistique du test est automatiquement standardisee (par rapport a un etalon) pour les modeles non-emboites et fait fi, asymptotiquement, des modeles emboites. Les auteurs illustrent leur approche a l'aide de donntes americaines de sinistres en assurance.

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