Variograms for spatial max-stable random fields

By Daniel Cooley, Philippe Naveau, Paul Poncet. 2006

230 citations recorded by the source corpus.

Subfields: Environmental Engineering, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/b2b42957dd92fa6a4c1deeec452aa769e3ed287f

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In Environmental Engineering

In Finance

In Management Science and Operations Research

Citations in the corpus

Conditional simulation of max-stable processes (2012, methodology): “…simulations of max-stable processes 3 Paralleling the use of the variogram in classical geostatistics, the extremal coefficient function (Schlather & Tawn, 2003; Cooley et al., 2006) θ(x1 − x2) = −z log pr{Z(x1) ≤ z, Z(x2) ≤ z} is widely used to summarize the spatial dependence of extremes.”
Extremes on river networks (2015, methodology): “In order to assess whether the Hüsler–Reiss distribution approximates the extremal dependence of our data well, we estimate the extremal coefficient (8) for each pair of locations by the madogram θ̂ (Cooley et al., 2006) based on summer maxima.”
Using Bayesian Kriging for Spatial Smoothing in Crop Insurance Rating (2018, methodology): “The sill parameter q involves the maximum limit of F-Madogram, which represents the maximum difference between the parameters in the different counties, and range parameter h involves the distance at which the FMadogram flattens out, which represents the distance that the spatial correlation remains”
Spatial extremes: Max-stable processes at work (2013, methodology): “As a substitute to the semi variogram, one can use the F-madogram Cooley et al. (2006) νF(x1− x2) = 1 2 E [|Fx1{Z(x1)}−Fx2{Z(x2)}”
Modeling the spatial dependence of floods using the Fisher copula (2019, methodology): “The F-madogram summarizes the spatial dependence structure of the data (Cooley et al., 2006) and is expressed as where the margin of Z(x) equals Fréchet margins, F(x) = exp ( − 1 /x) , and h is the distance between a pair of stations.”
Non-Stationary Dependence Structures for Spatial Extremes (2014, methodology): “, calculated using the F -madogram estimator (Cooley et al., 2006); however, simulations (not shown) have revealed that this approach induces a “selection bias”.”
Spatial Bayesian hierarchical modeling of precipitation extremes over a large domain (2015, background): “Max-stable processes [Schlather, 2002; Cooley et al., 2006; Shang et al., 2011; Ribatet et al., 2012; Padoan et al., 2010; Sang, 2015] refer to the specification of a joint distribution that is specifically formulated for spatial extreme data.”
Extreme value copulas and max-stable processes (2013, background): “When focusing on extreme value copulas, a convenient statistic to summarize the dependence is the extremal coefficient[28, 3].”
Bayesian hierarchical modeling of extreme hourly precipitation in Norway (2013, methodology): “The madogram (Cooley et al., 2006) is an analogue to the variogram that assesses spatial dependence in extreme values.”
Estimation of Hüsler–Reiss distributions and Brown–Resnick processes (2012, methodology): “the ‘madogram’ in Cooley et al. (2006), it is a common tool for model checking.”
Random Fields Simplified: Preserving Marginal Distributions, Correlations, and Intermittency, With Applications From Rainfall to Humidity (2020, background): “…extremes, extreme value theory also provides other options such as max‐stable processes and corresponding random fields (e.g., Blanchet & Davison, 2011; Cooley et al., 2006; Davison et al., 2012; Davison & Gholamrezaee, 2012; Robert, 2013; Martin Schlather, 2002; Tyralis & Langousis, 2019).”