An Introduction to Statistical Modeling of Extreme Values

By Stuart Coles. 2001

7,218 citations recorded by the source corpus.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/222449231d0720a982b44799041e6535c1fc0e2c

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Citations in the corpus

Estimating Mean Dimensionality of Analysis of Variance Decompositions (2006, methodology): “(A recent reference on extreme values is Coles 2001.) The mean dimension is a tractable tool for comparing results for different G. We find that the mean dimension depends very strongly on G. For some G, the mean dimension is close to d. We do not expect that the mean dimension can approach 1 as d →”
Human contribution to the European heatwave of 2003 (2004, positive): “6 K threshold from the generalized Pareto distribution (GPD) fitted to the HadCM3 control run temperature”
Estimating value-at-risk: a point process approach (2005, methodology): “For more details on the technical development of standard likelihood for a non-homogenous Poisson process, see Cox and Isham (1979), or Coles (2001) p.”
Multi-period hedge ratios for a multi-asset portfolio when accounting for returns comovement (2008, neutral): “9This is given by ⎪⎩ ⎪ ⎨ ⎧ =ζ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ β −−≠ζ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ β ζ +−= ζ− βζ 0,)u( yexp1;0, )u( y11)y(H /1 )u(, , where β(u)>0, and y≥0 when ζ≥0, and 0≤y≤−β(u)/ζ when ζ<0 (see, for example, Coles, 2001).”
Generalized Gumbel distribution (2010, background): “5.1 Wave and surge height data This data set is a concurrent measurement of two oceanographic variables – wave and surge height at a single location off south-west England [1].”
Spatial regression models for extreme precipitation in Belgium (2012, methodology): “The transformation R xið Þ ¼ 1g log 1þ g Z xið Þ m xið Þ s xið Þ ð21Þ results in a Gumbel distributed random variable R(xi) [Coles, 2001; Beirlant et al., 2004], i.e., F[R(xi) ≤ r] = exp[ exp( r)].”
The effect of horizontal resolution on simulation of very extreme US precipitation events in a global atmosphere model (2010, background): “In fact, GEV theory is an asymptotic treatment of the tails of distributions with relatively few restrictions on its validity (Coles 2001; Castillo et al. 2004).”
Statistical Methods for Nonstationary Extremes (2013, methodology): “Rather, we adopt a more pragmatic approach, with one or more of the parameters of the extremal distributions being expressed as functions of time (Coles 2001).”
Latency and Reliability-Aware Task Offloading and Resource Allocation for Mobile Edge Computing (2017, background): “Extreme value theory also provides statistical models for the computation of extreme risk measures [9].”
Use of a Gaussian copula for multivariate extreme value analysis: Some case studies in hydrology (2007, background): “Multivariate extreme value theory (MEVT) is studied by mathematicians (see Coles [6] for a review of the topic).”
Generalized maximum likelihood estimators for the nonstationary generalized extreme value model (2007, methodology): “…likelihood estimators of the nonstationary GEV model parameters can be determined by maximizing the likelihood function, given by the general form [Coles, 2001] Ln xjmt;at;ktð Þ ¼ Yn1 t¼1 1 at exp 1 kt xt mt at 1=kt( ) * 1 kt xt mt at 1 1ktð Þ * Yn t¼n1þ1 1 at exp xt mt at * exp exp xt mt…”
Extended generalised Pareto models for tail estimation (2011, methodology): “The practice of pooling parameters and more specifically of the tail index in the extreme value modelling framework can be found in various applications including Coles and Tawn (1990); Cooley et al. (2007) and Davison et al.”
Extreme Value Theory for Open Set Classification - GPD and GEV Classifiers (2018, neutral): “Theorem 2 ([23]) .”