A Euclidean Likelihood Estimator for Bivariate Tail Dependence

M. de Carvalho, B. Oumow, J. Segers, M. Warchol

Research output: Contribution to journalArticlepeer-review

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 ®]). 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.
Original languageEnglish
Pages (from-to)1176-1192
Number of pages17
JournalCommunications in Statistics - Theory and Methods
Volume42
Issue number7
DOIs
Publication statusPublished - 1 Apr 2013

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