Statistics of Extremes

By A. C. Davison. International Encyclopedia of Statistical Science, 2011

1,730 citations recorded by the source corpus.

Subfields: Atmospheric Science, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/43a81cf30ec1ea3052fbeb9f872c6963579096d1

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Citations in the corpus

Unified nano-mechanics based probabilistic theory of quasibrittle and brittle structures: I. Strength, static crack growth, lifetime and scaling (2011, background): “(2) Perfectly brittle structures, in which the failure localizes into one RVE and thus the failure of the entire structure is triggered by the failure of one RVE (like in a chain).”
Extrema of log-correlated random variables: Principles and Examples (2016, background): “ry was developed in the context of independent or weakly correlated random variables. The rst book regrouping the early advances in the eld is the still relevant Statistics of Extremes by E.J. Gumbel [43] published in 1958. Gumbel credits the rst work on extreme values to Bortkiewicz in 1898, which ”
Thermodynamics as a theory of decision-making with information-processing costs (2012, methodology): “The cumulative distribution function of choosing v after m draws is given by Fm(v) = F0(v) , (12) where F0 is the cumulative distribution function of μ [24].”
New asymptotic and preasymptotic results on rainfall maxima from multifractal theory (2009, background): “[3] The specific form of the distribution (EV1 when the shape parameter k = 0, EV2 when k > 0 and EV3 when k < 0) depends on the upper tail of the parent distribution, in our case the distribution of Id [Gumbel, 1958].”
COMPASS server for homology detection: improved statistical accuracy, speed and functionality (2009, background): “As a result, the statistical signiﬁcance can be estimated using extreme value distribution (EVD) (35,36).”
Likelihood‐based procedures for threshold diagnostics and uncertainty in extreme value modelling (2012, background): “A review of this second-order theory and further references are given in Beirlant et al. (2004).”
Modeling Spatial Processes with Unknown Extremal Dependence Class (2017, background): “(2012), Segers (2012), or Davison and Huser (2015) for recent reviews on max-stable models.”
A Horse Race between the Block Maxima Method and the Peak–over–Threshold Approach (2018, methodology): “1) gives rise to the block maxima method (BM) (Gumbel, 1958): for some block size r ∈ {1, .”
Weak convergence of the tail empirical process for dependent sequences (2009, background): “There are several recent books on the subject [7,23,26,27,2,34] and a large journal literature.”
Quantifying extreme behavior in geomagnetic activity (2011, background): “, Beirlant et al. [2004], Coles [2004], and Gilleland and Katz [2006] for an introduction).”
Maximum likelihood estimators based on the block maxima method (2017, methodology): “The Block Maxima (BM) method, also known as Annual Maxima, after Gumbel [11] is a fundamental method in Extreme Value Theory and has been widely used.”
Existence and consistency of the maximum likelihood estimators for the extreme value index within the block maxima framework (2015, background): “[2] or de Haan and Ferreira [5] provide good reviews on this estimation problem.”
Battle of extreme value distributions: A global survey on extreme daily rainfall (2013, background): “equivalently, that the underlying distribution is the Gumbel. It is highly probable for a null hypothesis with small values of , e.g., H0: 1⁄4 0.01 or H0: 1⁄4 0.01 not to be rejected. Hence, we deem that it is not possible to conclude with certainty applying statistical tests whether the underlying ”
Modelling across extremal dependence classes (2014, background): “The density of the associated measure Hη can be calculated as in Beirlant et al. (2004), section 9.”