New estimators of the Pickands dependence function and a test for extreme-value dependence
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Date
2010-05-31T09:35:59Z
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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
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Keywords
Copula process, Extreme-value copula, Minimum distance estimation, Pickands dependence function, Test for extreme-value dependence, Weak convergence