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On estimating extremal dependence structures by parametric spectral measures. (English) Zbl 1486.62138

Summary: Estimation of extreme value copulas is often required in situations where available data are sparse. Parametric methods may then be the preferred approach. A possible way of defining parametric families that are simple and, at the same time, cover a large variety of multivariate extremal dependence structures is to build models based on spectral measures. This approach is considered here. Parametric families of spectral measures are defined as convex hulls of suitable basis elements, and parameters are estimated by projecting an initial nonparametric estimator on these finite-dimensional spaces. Asymptotic distributions are derived for the estimated parameters and the resulting estimates of the spectral measure and the extreme value copula. Finite sample properties are illustrated by a simulation study.

MSC:

62G32 Statistics of extreme values; tail inference
62H05 Characterization and structure theory for multivariate probability distributions; copulas
62H12 Estimation in multivariate analysis
62E20 Asymptotic distribution theory in statistics
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