Nonparametric estimation of the dependence function for a multivariate extreme value distribution

By Dabao Zhang, Martin T. Wells, Liang Peng. 2008

57 citations recorded by the source corpus.

Understanding and modeling dependence structures for multivariate extreme values are of interest in a number of application areas. One of the well-known approaches is to investigate the Pickands dependence function. In the bivariate setting, there exist several estimators for estimating the Pickands dependence function which assume known marginal distributions [J. Pickands, Multivariate extreme value distributions, Bull. Internat. Statist. Inst., 49 (1981) 859-878; P. Deheuvels, On the limiting behavior of the Pickands estimator for bivariate extreme-value distributions, Statist. Probab. Lett. 12 (1991) 429-439; P. Hall, N. Tajvidi, Distribution and dependence-function estimation for bivariate extreme-value distributions, Bernoulli 6 (2000) 835-844; P. Caperaa, A.-L. Fougeres, C. Genest, A nonparametric estimation procedure for bivariate extreme value copulas, Biometrika 84 (1997) 567-577]. In this paper, we generalize the bivariate results to p-variate multivariate extreme value distributions with p>=2. We demonstrate that the proposed estimators are consistent and asymptotically normal as well as have excellent small sample behavior.

Subfields: Demography, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/8b481a97233351211f6662818ba6906de456e986

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Citations in the corpus

Multivariate multiparameter extreme value models and return periods: A copula approach (2010, methodology): “An alternative way to fit the parameters would be to use a( d − 1)‐variate version of Pickands’s dependence function, as outlined in some recent works [see Zhang et al., 2008; Genest and Segers, 2009].”
A goodness-of-fit test for bivariate extreme-value copulas (2011, background): “To see how the estimation can proceed in the d-variate case when the marginal distributions are known, refer to [39] or [21].”
Multivariate nonparametric estimation of the Pickands dependence function using Bernstein polynomials (2014, methodology): “represents a loss of generality. For this reason, several nonparametric estimators of the Pickands have been proposed, examples are: Pickands (1981), Caperaa et al. (1997), Hall and Tajvidi (2000), Zhang et al. (2008), Gudendorf and Segers (2011, 2012) to name a few. However, it has not been possibl”
New estimators of the Pickands dependence function and a test for extreme-value dependence (2011, background): “l variants have been discussed. Alternative estimators have been proposed and investigated in the papers by Caperaa et al. (1997), Jimenez et al. (2001), Hall and Tajvidi (2000), Segers (2007) and Zhang et al. (2008), where the last-named authors also discussed the multivariate case. In most referen”
Extreme-value copulas (2009, unknown): “For multivariate extensions, see [41, 94].”
RANK-BASED INFERENCE FOR BIVARIATE EXTREME-VALUE COPULAS (2007, unknown): “nd form of dependence (e.g., symmetry or lack thereof) on the precision of the various rank-based estimators proposed herein. Multivariate extensions could also be developed along similar lines as in Zhang et al. (2008). Finally, the problem of constructing a truly semiparametric eﬃcient estimator o”
Nonparametric estimation of multivariate extreme-value copulas (2011, methodology): “The multivariate extension of the CFG estimator waspre ented in Zhang et al. (2008), albeit under a different but equivalent form.”