Statistics of Extremes: Theory and Applications

By Jan Beirlant, Yuri Goegebeur, Johan Segers, Jozef L. Teugels. 2004

122 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/acf1ca2e3e12bb15f610e68b6df75adbc0dff610

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Citations in the corpus

Multivariate extremes and the aggregation of dependent risks: examples and counter-examples (2009, unknown): “For the converse, see Beirlant et al. (2004), Section 8.2.7.”
Maximum Empirical Likelihood Estimation of the Spectral Measure of an Extreme Value Distribution (2008, unknown): “For a general background on spectral measures and these dependence functions as well as results for the corresponding estimators, see for instance the monographs Coles (2001), Beirlant et al. (2004) and de Haan and Ferreira (2006). An alternative to the nonparametric approach in this paper is the pa”
An M-Estimator for Tail Dependence in Arbitrary Dimensions (2011, unknown): “∞)} such that (1) l(x) = Λ {u∈ [0,∞]d : u1 6 x1 or ... or ud 6 xd} , (2) Λ(tA) = tΛ(A), for any t>0 and any Borel set A⊂ [0,∞]d \{(∞,...,∞)}, where tA:= {tx: x∈ A}, see for example Resnick (1987), Beirlant et al. (2004), de Haan and Ferreira (2006). The measure Λ is called the exponent measure an”
Extremiles: A New Perspective on Asymmetric Least Squares (2018, methodology): “Thorough discussions on the interpretation and the rationale behind this condition can be found in the monographs of Beirlant et al. (2004) and de Haan and Ferreira (2006), along with abundant examples of commonly used continuous distributions satisfying (12).”
Estimation of the marginal expected shortfall: the mean when a related variable is extreme (2012, background): “…for all ( x; y ) ∈ [0 ; ∞ ] 2 \ { (+ ∞ ; + ∞ ) } ; the following limit exists: ( x; y ) : (1) The function R completely determines the so-called stable tail dependence function l , as for all x; y ≥ 0, l ( x; y ) = x + y − R ( x; y ); see Drees and Huang (1998); Beirlant et al. (2004, Chapter 8.2).”
A continuous updating weighted least squares estimator of tail dependence in high dimensions (2016, background): “For more background on multivariate extreme value theory, see for instance Beirlant et al. (2004) or de Haan and Ferreira (2006).”
Statistical concepts of a priori and a posteriori risk classification in insurance (2011, unknown): “See Beirlant et al. (2004) for an example demonstrating its usefulness using losses from a reinsurance company.”
Convex geometry of max-stable distributions (2006, unknown): “ar X iv :m at h/ 06 03 42 3v 3 [ m at h. PR ] 2 Keywords: copula; max-stable random vector; norm; cross-polytope; spectral measure; support function; zonoid”
Multivariate peaks over thresholds models (2016, unknown): “goodness of t checking. The nal contribution of this paper is a number of simulation algorithms for multivariate GP distributions. The multivariate GP distributions were introduced in Tajvidi (1996), Beirlant et al. (2004, Chapter 8), and Rootzen and Tajvidi (2006); see also Falk et al. (2010, Chapt”
Estimation of tail risk based on extreme expectiles (2016, unknown): “As in Beirlant et al. (2004), we only deal here with the 75,789 claims for 1991.”
Space–time modelling of extreme events (2012, methodology): “Alternative approaches recently proposed are based on generalized Pareto processes (Ferreira and de Haan, 2012; Aulbach and Falk, 2012) and multivariate generalized Pareto distributions (Rootzén and Tajvidi (2006), Buishand et al. (2008) and Beirlant et al. (2004), page 277).”