Maximum Empirical Likelihood Estimation of the Spectral Measure of an Extreme Value Distribution

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AMS 2000 subject classifications: Primary 62G05, 62G30, 62G32; secondary 60G70, 60F05, 60F17, JEL: C13, C14.

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Dimension reduction in multivariate extreme value analysis (2015, methodology): “In the bivariate setting, many estimators were proposed to assess this angular measure (Beirlant et al., 2004; Einmahl and Segers, 2009; Einmahl et al., 2001; Resnick, 2007).”
Statistical Modeling of Spatial Extremes (2012, background): “…(Kotz and Nadarajah (2000), Section 3.5), those in current use tend to be somewhat inflexible, and, owing to the curse of dimensionality, nonparametric estimation has essentially been confined to the bivariate case (Fougères (2004); Boldi and Davison (2007); Einmahl and Segers (2009)).”
A Horse Race between the Block Maxima Method and the Peak–over–Threshold Approach (2018, methodology): “…case, the literature on further theoretical foundations for the multivariate POT method is vast, see, e.g., Einmahl, de Haan and Piterbarg (2001); Einmahl and Segers (2009) for nonparametric estimation of the spectral measure, Drees and de Haan (2015) for estimation of failure probabilities, or…”
Spectral Density Ratio Models for Multivariate Extremes (2014, methodology): “The one-sample empirical likelihood estimator Ḧk (Einmahl and Segers, 2009) provides a benchmark to verify whether the specification of the weight function g(w,ψk) is appropriate.”
Extreme-value copulas (2009, background): “See for instance [5, 13, 49, 24, 59, 60, 61, 63] for some (semi-)parametric approaches and [1, 6, 23, 22, 25, 81] for some nonparametric ones.”