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 |
URI: | http://hdl.handle.net/2003/27248 http://dx.doi.org/10.17877/DE290R-8728 |
Issue Date: | 2010-05-31T09:35:59Z |
Appears in Collections: | Sonderforschungsbereich (SFB) 823 |
Files in This Item:
File | Description | Size | Format | |
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DP_2110_Bücher_Dette_Volgushev.pdf | DNB | 1.02 MB | Adobe PDF | View/Open |
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