Statistics of Extremes

By Jan Beirlant. 2004

1,023 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b68b830018b8f4d393de27f976aa1094e43652eb

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Citations in the corpus

A Hierarchical Model for Serially-Dependent Extremes: A Study of Heat Waves in the Western US (2014, neutral): “…(s1, . . . , sJ ) and cut-offs x = (x1, . . . , xJ ) we show in the Supplementary Materials that the joint distribution is P(Xs1 ≤ x1, . . . ,XsJ ≤ xJ ) = exp [−V (s,x)], (2.3) where V (s,x) = ∑Ll=1[∑Jj=1 x−1/αj Kl(sj |γ )1/α]α is the J -dimensional exponent measure function (Beirlant et al. 2004).”
A two-step framework for over-threshold modelling of environmental extremes (2014, background): “An attempt to cope at the same time with EVT and autocorrelated data is the introduction of the extremal index, (Leadbetter et al., 1983; Smith and Weissman, 1994; Embrechts et al., 1997; Ancona-Navarrete and Tawn, 2000; Coles, 2001; Beirlant et al., 2004).”
Bayesian inference for long-term prediction of significant wave height (2007, methodology): “An alternative approach is to use Extreme Value Theory (EVT) (e.g., Embrechts et al., 1997; Coles, 2001; Beirlant et al., 2004; Castillo et al., 2004) which provides simple techniques for estimating probabilities of future extreme wave measurements given historical data.”
A Horse Race between the Block Maxima Method and the Peak–over–Threshold Approach (2018, methodology): “Similar to the discussion on the location and scale parameters in the univariate case, the objects that are estimated by POT and BM may be different but are linked by the multivariate extremal index (Nandagopalan, 1994, see also Section 10.5 in Beirlant et al., 2004).”
Extreme Value Theory for Finance: A Survey (2012, background): “For a systematic and detailed account of EVT and its applications many books are now available, e.g.: Beirlant et al. (2004); Coles (2001); de Haan and Ferreira (2006); Embrechts et al. (1997); Falk et al. (2004); Finkenstädt and Rootzén (2004); Galambos (1987); Kotz and Nadarajah (2000);…”
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).”
Second-order refined peaks-over-threshold modelling for heavy-tailed distributions (2009, result): “371 = 0.81%. In comparison to the Weissman (Hill) and POT (GPD) estimates, the trajectories of the EPD estimates are relatively stable, with γˆ around 0.3 and p around 0.75%. By way of comparison, in Beirlant et al. (2004, Section 6.2.4) it is suggested to model the complete distribution by a mixtur”
An efficient semiparametric maxima estimator of the extremal index (2015, background): “Following (Beirlant et al, 2004, chapter 10) G(x) = P (X1 6 x, . . . , Xb 6 x), = P (X1 6 x, θZ2 6 x, . . . , θZb 6 x), = exp {− [1 + θ(b− 1)] /x} .”
Functional peaks‐over‐threshold analysis (2020, methodology): “The max-domain of attraction conditions are broadly but not universally satisfied (e.g., Beirlant et al., 2004, pp. 59, 62, 72).”
Statistical Modelling of Spatial Extremes (2012, background): “Systematic mathematical accounts are given by Resnick (1987, 2006) and de Haan and Ferreira (2006), while more statistical treatments may be found in Beirlant et al. (2004), Coles (2001) and Embrechts et al. (1997), the last focusing particularly on finance.”
Statistical concepts of a priori and a posteriori risk classification in insurance (2011, background): “See Beirlant et al. (2004) for an example demonstrating its usefulness using losses from a reinsurance company.”