Nonparametric estimation of multivariate extreme-value copulas
(2012) Journal of Statistical Planning and Inference — Vol. 142, n° 12, p. 3073-3085 (2012)
Files
RP_2012_11_segers_nonparametric_estimation.pdf
Closed Access - Adobe PDF
- 378.48 KB
Details
- Authors
- Abstract
- 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.
- Affiliations
Citations
Gudendorf, G., & Segers, J. (2012). Nonparametric estimation of multivariate extreme-value copulas. Journal of Statistical Planning and Inference, 142(12), 3073-3085. https://doi.org/10.1016/j.jspi.2012.05.007 (Original work published 2012)