Nonparametric estimation of the spectral measure of an extreme value distribution

By John H. J. Einmahl, Laurens de Haan, V. Piterbarg. 2001

128 citations recorded by the source corpus.

Subfields: Finance, Global and Planetary Change, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c87d6934584915cfa70b33d653cc4a1e1293ee07

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Citations in the corpus

Dimension reduction in multivariate extreme value analysis (2015, background): “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).”
Non‐parametric Estimation of Tail Dependence (2006, methodology): “Einmahl et al. (2001) propose a non-parametric estimator for the above spectral measure : ̂m( )= 1k m∑ j=1 1{ R(j)m1∨R (j) m2≥m+1−k, arctan m+1−R(j)m2 m+1−R(j)m1 ≤ } for ∈ [0, /2] and discuss the related asymptotic properties.”
Regularly varying multivariate time series (2007, background): “This phenomenon was already discovered for squared ARCH(1) processes in de Haan et al. (1989) and described for general univariate Markov processes in Smith (1992) and Perfekt (1994); see also Perfekt (1997), Yun (1998, 2000), Bortot and Coles (2003) and Segers (2007).”
Weighted approximations to tail copula processes with application to testing the extreme value condition (2006, unknown): “5) holds with α = 2 (see [8], pages 1409–1410).”
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.”
Semi‐Parametric Models for the Multivariate Tail Dependence Function – the Asymptotically Dependent Case (2008, background): “Key words: asymptotic normality, dependence modelling, elliptical copula, elliptical distribution, regular variation, semi-parametric model, tail dependence function”
On the foundations of multivariate heavy-tail analysis (2004, methodology): “A method based on ranks (see [24], [48]) overcomes some of the discomfort inherent in tail estimation since it does not require marginal tail estimates.”