New estimators of the Pickands dependence function and a test for extreme-value dependence
| dc.contributor.author | Bücher, Axel | |
| dc.contributor.author | Dette, Holger | |
| dc.contributor.author | Volgushev, Stanislav | |
| dc.date.accessioned | 2010-05-31T09:35:59Z | |
| dc.date.available | 2010-05-31T09:35:59Z | |
| dc.date.issued | 2010-05-31T09:35:59Z | |
| dc.description.abstract | We 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 62G20 | en |
| dc.identifier.uri | http://hdl.handle.net/2003/27248 | |
| dc.identifier.uri | http://dx.doi.org/10.17877/DE290R-8728 | |
| dc.language.iso | en | en |
| dc.relation.ispartofseries | Discussion Paper / SFB 823;21/2010 | |
| dc.subject | Copula process | en |
| dc.subject | Extreme-value copula | en |
| dc.subject | Minimum distance estimation | en |
| dc.subject | Pickands dependence function | en |
| dc.subject | Test for extreme-value dependence | en |
| dc.subject | Weak convergence | en |
| dc.subject.ddc | 310 | |
| dc.subject.ddc | 330 | |
| dc.subject.ddc | 620 | |
| dc.title | New estimators of the Pickands dependence function and a test for extreme-value dependence | en |
| dc.type | Text | de |
| dc.type.publicationtype | report | de |
| dcterms.accessRights | open access |