Statistics of Extremes: Theory and Applications

By Nicole A. Lazar. Technometrics, 2005

1,017 citations recorded by the source corpus.

Subfields: Atmospheric Science, Electrical and Electronic Engineering, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/431f41747a00785070d70dc16eb63f2054c216da

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Citations in the corpus

Extreme Value Analysis: an Introduction (2013, methodology): “We have the following result (see Theorem 2.3 in Section 2.6 in Beirlant et al. (2004b)) Theorem 2.6.”
FITTING MIXTURES OF ERLANGS TO CENSORED AND TRUNCATED DATA USING THE EM ALGORITHM (2015, methodology): “When modeling the Secura Re data of the previous example using Pareto-type modeling, Beirlant et al. (2004) estimate the corresponding EVI around 0.3.”
Forecast verification: current status and future directions (2008, methodology): “Extreme value modelling approaches use a subset of large values from the data sample to infer the extreme properties of the underlying process that generated the data (e.g. Coles, 2001; Beirlant et al., 2004).”
Multivariate goodness-of-fit tests based on Wasserstein distance (2020, background): “Each Pθ ∈ M is thus a d-variate max-stable distribution, that is, a possible large-sample limit of the vector of affinely normalized component-wise maxima of an i.i.d. sample from a common distribution (Beirlant et al., 2004, Chapter 9).”
Extreme-value copulas (2009, background): “For more extensive overviews, see e.g. [3, 62].”
Concentration inequalities in the infinite urn scheme for occupancy counts and the missing mass, with applications (2014, background): “[7]): harnessing limiting expressions and tail parameter estimation.”
An M‐estimator of spatial tail dependence (2014, background): “For more examples and background on multivariate extreme value theory, see Coles (2001), Beirlant et al. (2004) or de Haan and Ferreira (2006).”
Maximum likelihood estimators based on the block maxima method (2017, background): “[2], de Haan and Ferreira [6] and references therein.”
A new class of models for bivariate joint tails (2009, methodology): “An alternative treatment of the links between BEV models and our representation was given by Beirlant et al. (2004), example 9.7; however, they did not make a direct comparison of the two normalization conditions.”
Bayesian composite marginal likelihoods (2011, background): “Non-parametric estimation has been proposed in the literature (see, e.g., Beirlant et al. (2004)), but it is difficult to implement when, as is common in the field of extremes, few observations are available.”
Community detection in graphs (2009, methodology): “This probability is computed by using tools from Extreme and Order Statistics (Beirlant et al., 2004; David and Nagaraja, 2003).”
Continuous Spatial Process Models for Spatial Extreme Values (2010, background): “The latter is a well studied problem with a long history (see, e.g., Beirlant (2004), for details and development), allowing both asymptotic dependence and independence.”
A new representation for multivariate tail probabilities (2013, background): “[1], Chapter 9, for a review of available methodology), whilst the sets nB, logn + A become some extreme sets B ⊆ [1,∞](2) and A ⊆ [0,∞](2).”
Statistical Modeling of Spatial Extremes (2012, background): “Systematic mathematical accounts are given by Resnick (1987, 2007) and de Haan and Ferreira (2006), while more statistical treatments may be found in Beirlant et al. (2004), Coles (2001) and Embrechts, Klüppelberg and Mikosch (1997), the last focusing particularly on finance.”
Multivariate nonparametric estimation of the Pickands dependence function using Bernstein polynomials (2014, background): “, Xd) be a d-dimensional random vector of maxima that follows a multivariate max-stable distribution G; for more background on univariate and multivariate extreme-value theory, see for instance Beirlant et al. (2004), de Haan and Ferreira (2006), or Falk, Hüsler, and Reiss (2010).”
Nonparametric regression estimation of conditional tails: the random covariate case (2014, background): “In fact, after some straightforward simplification of (4), one easily sees that condition (R2) makes the convergence in (2) explicit.”
Multivariate non-normally distributed random variables in climate research - introduction to the copula approach (2008, background): “In order to characterize the limit behavior of multivariate extremes, it has been shown, that weak convergence of the multivariate distribution is equivalent to weak convergence of the marginals as well as the copula function, provided that the marginals are continuous (Beirlant et al., 2004).”