Nonparametric estimation of multivariate extreme-value copulas

By Gordon Gudendorf, Johan Segers. 2011

65 citations recorded by the source corpus.

Extreme-value copulas arise in the asymptotic theory for componentwise maxima of independent random samples. An extreme-value copula is determined by its Pickands dependence function, which is a function on the unit simplex subject to certain shape constraints that arise from an integral transform of an underlying measure called spectral measure. Multivariate extensions are provided of certain rank-based nonparametric estimators of the Pickands dependence function. The shape constraint that the estimator should itself be a Pickands dependence function is enforced by replacing an initial estimator by its best least-squares approximation in the set of Pickands dependence functions having a discrete spectral measure supported on a sufficiently fine grid. Weak convergence of the standardized estimators is demonstrated and the finite-sample performance of the estimators is investigated by means of a simulation experiment.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/431645fe6470dcb99e69c9fa6e452444ab2cb1cd

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

In Statistics and Probability

Citations in the corpus

Multivariate nonparametric estimation of the Pickands dependence function using Bernstein polynomials (2014, methodology): “For comparison purposes we have also considered the weighted and endpoint-corrected versions of the P and CFG estimators as discussed in Gudendorf and Segers (2012), denoted by Pw and CFGw respectively.”
A Horse Race between the Block Maxima Method and the Peak–over–Threshold Approach (2018, background): “See, for instance, Pickands (1981); Capéraà, Fougères and Genest (1997); Zhang, Wells and Peng (2008); Genest and Segers (2009); Gudendorf and Segers (2012) for nonparametric estimators and Genest, Ghoudi and Rivest (1995); Dombry, Engelke and Oesting (2016) for parametric ones, among many…”
Probit Transformation for Nonparametric Kernel Estimation of the Copula Density (2014, background): “…(2004), Tsukuhara (2005), Segers (2012) and Bücher and Volgushev (2013), and turns out to be the cornerstone of a variety of nonparametric copula-based procedures, see e.g. Genest and Rémillard (2004), Genest et al (2009a), Gudendorf and Segers (2012) or Li and Genton (2013), to cite only a few.”