Models for Stationary Max-Stable Random Fields

By Martin Schlather. 2002

497 citations recorded by the source corpus.

Subfields: Atmospheric Science, Finance, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/6680ebb274c40efe7c566d799edab0b16a0a5772

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Citations in the corpus

On spatial extremes: With application to a rainfall problem (2008, methodology): “Coles and Tawn, in a series of papers [Coles (1993), Coles and Tawn (1996)], have developed methods to deal with spatial extremes based on the spectral representation [de Haan (1984), see also Schlather (2002)].”
Generalized Additive Models for Exceedances of High Thresholds With an Application to Return Level Estimation for U.S. Wind Gusts (2019, background): “Max-stable processes are a complementary branch of multivariate extreme value model, which in the present context may be classed as residual models; see Smith (1990) and Schlather (2002) for examples and Davison and Gholamrezaee (2012) for a summary.”
Conditional simulation of max-stable processes (2012, methodology): “For examples of non-regular cases and conditional sampling procedures in these cases, see Wang and Stoev (2011) and Oesting and Schlather (2014) who consider max-linear and mixed moving maxima processes, respectively.”
Conditional sampling for spectrally discrete max-stable random fields (2010, background): “[2], Schlather [22], Schlather and Tawn [23], Cooley et al.”
Spatial Bayesian hierarchical modeling of precipitation extremes over a large domain (2015, methodology): “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.”
Max-stable processes for modelling extremes observed in space and time (2011, methodology): “Max-stable processes based on space-time correlation functions Before presenting the construction of a max-stable space-time process, we begin with the definition of the Brown-Resnick space-time process with Fréchet marginals (see Brown and Resnick [5] or Schlather [38]).”
Graphical models for extremes (2018, background): “1/∈ [1, d] is known as the d-variate extremal coefficient (see Schlather and Tawn (2003)).”
Non-Stationary Dependence Structures for Spatial Extremes (2014, methodology): “ max-stable process. Standardization allows the treatment of the margins to be separated from the dependence structure. Simple max-stable processes have been characterized by de Haan (1984); see also Schlather (2002) and de Haan and Ferreira (2006, x9.4). Given points fP i;i= 1;2;:::gof a Poisson pr”
Asymptotic models and inference for extremes of spatio-temporal data (2010, methodology): “Another alternative is to use a spatial Gaussian process (see Schlather 2002 for details).”
Estimation of Hüsler–Reiss distributions and Brown–Resnick processes (2012, unknown): “Schlather Table 1. Estimation results. The values for the standard deviation are obtained from simulating and re-estimating the respective models 100 times. estimator α s β c θ̂PROJ, LS 0.296 (0.0193) 0.234 (0.0744) 0.379 (0.532) 1.67 (0.1761) θ̂SPEC 0.338 (0.0166) 0.687 (0.1797) 0.456 (0.439) 2.21 ”
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): “The second type proposed by [ Sch02 ] stems from a Gaussian random field which is then scaled by the realization of a point process on (0, ∞):”
Extremes on river networks (2015, methodology): “…space R2 is the class of max-stable processes, giving several flexible models whose dependence is parameterized in terms of covariance functions [Schlather (2002), Opitz (2013)] or of negative definite kernels [Brown and Resnick (1977), Kabluchko, Schlather and de Haan (2009), Kabluchko (2011)].”
Spatial modeling of extreme snow depth (2011, methodology): “They are based on the Smith (1990) and Schlather (2002) max-stable representations, designed to model extreme snow depth explicitly.”