New estimators of the Pickands dependence function and a test for extreme-value dependence

By Axel Bucher, Holger Dette, Stanislav Volgushev. 2011

80 citations recorded by the source corpus.

We propose a new class of estimators for Pickands dependence function which is based on the best L 2 -approximation of the logarithm of the copula by logarithms of extremevalue copulas. An explicit integral representation of the best approximation is derived and it is shown that this approximation satises 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 p nf ^ A(t) A(t)g t2[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.

Subfields: Finance, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e00556cb2589623335414d6a20f351278de6bf69

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Citations in the corpus

Nonparametric estimation of multivariate extreme-value copulas (2011, methodology): “Finally, a new type of nonparametric estimator has been proposed in Bücher et al. (2011) for the bivariate case.”
Multivariate nonparametric estimation of the Pickands dependence function using Bernstein polynomials (2014, background): “c estimators of the Pickands dependence function have been proposed: see for instancePickands (1981), Caperaa et al. (1997),Hall and Tajvidi (2000),Zhang et al. (2008),Genest and Segers (2009),Buc her et al. (2011),Gudendorf and Segers(2011,2012), andBerghaus et al. (2013). All of these estimators r”