Nonparametric estimation of multivariate extreme-value copulas

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.

• metadata
• relations

Document type	Article de périodique (Journal article) – Article de recherche
Access type	Accès interdit
Publication date	2012
Language	Anglais
Journal information	"Journal of Statistical Planning and Inference" - Vol. 142, no.12, p. 3073-3085 (2012)
Peer reviewed	yes
Publisher	Elsevier BV * North-Holland ((Netherlands) Amsterdam)
issn	0378-3758
e-issn	1873-1171
Publication status	Publié
Affiliation	UCL - SSH/LIDAM/ISBA - Institut de Statistique, Biostatistique et Sciences Actuarielles
Keywords	Empirical copula ; Extreme-value copula ; Pickands dependence function ; Simplex ; Shape constraints ; Spectral measure ; Weak convergence
Links	http://hdl.handle.net/2078.1/127114[Handle] https://doi.org/10.1016/j.jspi.2012.05.007[DOI]

See also
	[boreal:78946]	Nonparametric estimation of multivariate extreme-value copulas