A Euclidean Likelihood Estimator for Bivariate Tail Dependence |
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| Authors: | Miguel de Carvalho Boris Oumow Johan Segers Micha? Warcho? |
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| Institution: | 1. Pontificia Universidade Católica de Chile , Santiago , Chile;2. Centro de Matemática e Aplica??es , Universidade Nova de Lisboa , Lisboa , Portugal mdecarvalho@mat.puc.cl;4. Ecole Polytechnique Fédérale de Lausanne , Lausanne , Switzerland;5. Université catholique de Louvain , Louvain-la-Neuve , Belgium |
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| Abstract: | The spectral measure plays a key role in the statistical modeling of multivariate extremes. Estimation of the spectral measure is a complex issue, given the need to obey a certain moment condition. We propose a Euclidean likelihood-based estimator for the spectral measure which is simple and explicitly defined, with its expression being free of Lagrange multipliers. Our estimator is shown to have the same limit distribution as the maximum empirical likelihood estimator of Einmahl and Segers (2009
Einmahl , J. H. J. ,
Segers , J. ( 2009 ). Maximum empirical likelihood estimation of the spectral measure of an extreme-value distribution . Ann. Statist. 37 ( 5B ): 2953 – 2989 .Crossref], Web of Science ®] , Google Scholar]). Numerical experiments suggest an overall good performance and identical behavior to the maximum empirical likelihood estimator. We illustrate the method in an extreme temperature data analysis. |
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| Keywords: | Bivariate extremes Empirical likelihood Euclidean likelihood Spectral measure Statistics of extremes |
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