A dependence measure for multivariate and spatial extreme values: Properties and inference

By Martin Schlather, Jonathan A. Tawn. 2003

309 citations recorded by the source corpus.

Subfields: Demography, Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/aed84bdaea853446295b840cd22ce5e4162d0238

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Citations in the corpus

Extremes on river networks (2015, background): “In the bivariate case m= 2, a common summary statistic for the dependence among components of FZ is the extremal coefficient θ ∈ [1,2] [see, e.g., Schlather and Tawn (2003)], which is defined through the expression P(Z1 ≤ u,Z2 ≤ u) = P(Z1 ≤ u)θ, u > 0,(8) or, equivalently, θ = V (1,1).”
Geostatistics of extremes (2012, methodology): “Thus, qD may be interpreted as the effective number of independent Frechét variables in the set indexed by D. Schlather & Tawn (2003) consider the constraints that must be satisfied by the extremal coefficients corresponding to different subsets of D, and show how the coefficients may be estimated…”
Likelihood-Based Inference for Max-Stable Processes (2009, methodology): “Schlather and Tawn (2003) discuss the extremal coefficient within the context of max-stable processes.”
Variograms for spatial max-stable random fields (2006, background): “Using the madogram, we can show, in a different way, some of propositions obtained by [ Sch03 ], but our proofs are much shorter and simpler.”
Geostatistics of Dependent and Asymptotically Independent Extremes (2013, background): “Analogues to θ(h) may be defined for more than two sites (Schlather and Tawn 2003), and are useful for model-checking.”
Multivariate non-normally distributed random variables in climate research - introduction to the copula approach (2008, background): “Much work in multivariate extreme value theory has centered around describing the dependence of extreme observations de Haan and Resnick (1993); Coles and Tawn (1996); Coles et al. (1999); Schlather and Tawn (2003); Heffernan and Tawn (2004); Mendes et al. (2006).”
Max-stable processes for modelling extremes observed in space and time (2011, background): “Examples include Coles [6] and Coles and Tawn [8], who model extremal rainfall fields using max-stable processes.”
Statistical Modelling of Spatial Extremes (2012, background): “Schlather and Tawn (2003) discuss the consistency properties that must be satisfied by the extremal coefficients of subsets of Z1, . . . , ZD, and suggest how these coefficients may be estimated.”
Ergodic properties of max-infinitely divisible processes (2009, unknown): “Note also that the sequence r(t) is positive–definite (see [24] or [26]) and hence, by Bochner’s theorem, there is a symmetric with respect to 0 measure μ on [−π, π] (called the spectral measure of X) such that r(t) = ∫ π −π e dμ(x) for all t ∈ Z.”
A conditional approach for multivariate extreme values (with discussion) (2004, background): “Accurate assessments of the probabilities of extreme events are sought in a diversity of applications from environmental impact assessment (Coles and Tawn, 1994; Joe, 1994; de Haan and de Ronde, 1998; Schlather and Tawn, 2003) to financial risk management (Embrechts et al.”
Spatial modeling of extreme snow depth (2011, methodology): “…on the quality of the selected model, we compare its predicted extremal coefficients, obtained by replacing the parameters involved in (9) by their estimates from Table 1, with the naive estimators of Schlather and Tawn (2003) or the madogram-based estimator of Cooley, Naveau and Poncet (2006).”
Spatial extremes: Max-stable processes at work (2013, background): “One convenient way to summarize the dependence structure of max-stable process Z is through its extremal coefficient function Schlather and Tawn (2003) θ(x1− x2) =−z logPr{Z(x1)≤ z,Z(x2)≤ z}= E [max{Y (x1),Y (x2)}} .”
Stationary max-stable fields associated to negative definite functions. (2008, unknown): “A natural dependence measure between η(0) and η(t) is given by ρ(t) = 2− ς(t) ∈ [0,1], where ς(t) is determined from the condition P[η(0) ≤ z, η(t) ≤ z] = P[η(0) ≤ z] for some (and hence all) z ∈ R; see, for example, [7, 28].”