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dc.contributor.authorBücher, Axel-
dc.contributor.authorDette, Holger-
dc.contributor.authorVolgushev, Stanislav-
dc.description.abstractWe propose a new class of estimators for Pickands dependence function which is based on the best L2-approximation of the logarithm of the copula by logarithms of extreme-value copulas. An explicit integral representation of the best approximation is derived and it is shown that this approximation satisfies the boundary conditions of a Pickands dependence function. The estimators A^(t) are obtained by replacing the unknown copula by its empirical counterpart and weak convergence of the process A^(t)A(t)gt2[0;1] is shown. A comparison with the commonly used estimators is performed from a theoretical point of view and by means of a simulation study. Our asymptotic and numerical results indicate that some of the new estimators outperform the rank-based versions of Pickands estimator and an estimator which was recently proposed by Genest and Segers (2009). As a by-product of our results we obtain a simple test for the hypothesis of an extreme-value copula, which is consistent against all alternatives with continuous partial derivatives of rst order satisfying C(u; v) uv. AMS Subject classification: Primary 62G05, 62G32; secondary 62G20en
dc.relation.ispartofseriesDiscussion Paper / SFB 823;21/2010-
dc.subjectCopula processen
dc.subjectExtreme-value copulaen
dc.subjectMinimum distance estimationen
dc.subjectPickands dependence functionen
dc.subjectTest for extreme-value dependenceen
dc.subjectWeak convergenceen
dc.titleNew estimators of the Pickands dependence function and a test for extreme-value dependenceen
dcterms.accessRightsopen access-
Appears in Collections:Sonderforschungsbereich (SFB) 823

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