Abstract
The extremal dependence structure of a regularly varying random vector is fully described by its limiting spectral measure. In this paper, we investigate how to recover characteristics of the measure, such as extremal coefficients, from the extremal behaviour of convex combinations of components of . Our considerations result in a class of new estimators of moments of the corresponding combinations for the spectral vector. We show asymptotic normality by means of a functional limit theorem and, focusing on the estimation of extremal coefficients, we verify that the minimal asymptotic variance can be achieved by a plug-in estimator using subsampling bootstrap. We illustrate the benefits of our approach on simulated and real data.
Funding Statement
The work of MO was partially supported by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC 2075—390740016.
OW acknowledges the support of the French Agence Nationale de la Recherche (ANR) under reference ANR20-CE40-0025-01 (T-REX project).
Acknowledgements
The authors are grateful to three anonymous referees and an Associate Editor for their valuable comments and suggestions.
The second author is also affiliated with Wolfgang Pauli Institut, c/o Fakultät für Mathematik, Universität Wien.
Citation
Marco Oesting. Olivier Wintenberger. "Estimation of the spectral measure from convex combinations of regularly varying random vectors." Ann. Statist. 52 (6) 2529 - 2556, December 2024. https://doi.org/10.1214/24-AOS2387
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