Authors: Bücher, Axel
Dette, Holger
Volgushev, Stanislav
Title: New estimators of the Pickands dependence function and a test for extreme-value dependence
Language (ISO): en
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
Subject Headings: Copula process
Extreme-value copula
Minimum distance estimation
Pickands dependence function
Test for extreme-value dependence
Weak convergence
Issue Date: 2010-05-31T09:35:59Z
Appears in Collections:Sonderforschungsbereich (SFB) 823

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