Spatial extremes: Models for the stationary case

By Laurens de Haan, T. Pereira. 2006

128 citations recorded by the source corpus.

The aim of this paper is to provide models for spatial extremes in the case of stationarity. The spatial dependence at extreme levels of a stationary process is modeled using an extension of the theory of max-stable processes of de Haan and Pickands [Probab. Theory Related Fields 72 (1986) 477-492]. We propose three one-dimensional and three two-dimensional models. These models depend on just one parameter or a few parameters that measure the strength of tail dependence as a function of the distance between locations. We also propose two estimators for this parameter and prove consistency under domain of attraction conditions and asymptotic normality under appropriate extra conditions.

Subfields: Applied Mathematics, Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/0d2ae4831aeb606e6aa0227290533e1f7a3aaf6a

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Citations in the corpus

Statistical Modeling of Spatial Extremes (2012, methodology): “The exponent measures for the Student and Laplace densities were derived by de Haan and Pereira (2006) but are appreciably more complicated and do not seem to have been used in applications. A second possibility is to take the {Wj(x)} to be stationary standard Gaussian processes with correlation fun”
Asymptotic models and inference for extremes of spatio-temporal data (2010, background): “See for example, de Haan and Ferreira (2006) or de Haan and Pereira (2006).”
An application of Bayesian analysis and Markov chain Monte Carlo methods to the estimation of a regional trend in annual maxima (2006, methodology): “Specific methods have thus been studied for modeling spatial extremes [Schalther and Tawn, 2003; Naveau et al., 2005; De Haan and Pereira, 2006].”
Spatial modeling of extreme snow depth (2011, methodology): “Smith’s model (4) corresponds to taking f to be a multivariate normal density, extended by de Haan and Pereira (2006) to Student t and Laplace densities.”
A continuous updating weighted least squares estimator of tail dependence in high dimensions (2016, background): “In fact, Smith (1990) already proposes an estimator based on pairwise ( | J | = 2) extremal coeﬃcients; see also de Haan and Pereira (2006) and Oesting et al. (2015).”
Conditional simulation of max-stable processes (2012, unknown): “To bypass this hurdle, de Haan & Pereira (2006) propose a semiparametric estimator and Padoan et al. (2010) suggest the use of the maximum pairwise likelihood estimator.”
Bayesian Inference from Composite Likelihoods, with an Application to Spatial Extremes (2009, background): “…for complex rare events, but for which closed forms are typically available only for the bivariate marginal densities [Smith, 1990; Schlather, 2002; de Haan and Pereira, 2006; Kabluchko et al., 2009], though Genton et al. [2011] show that substantial eﬃciency gains are possible if trivariate…”
Statistical Modelling of Spatial Extremes (2012, methodology): “The exponent measures for the Student and Laplace densities were derived by de Haan and Pereira (2006) but are appreciably more complicated and do not seem to have been used in applications. A second possibility is to take the {Wj(x)} to be stationary standard Gaussian processes with correlation fun”
Simulation of Brown–Resnick processes (2012, unknown): “Further models are given in Schlather (2002) and de Haan and Pereira (2006), see also de Haan and Ferreira (2006).”
Geostatistics of extremes (2012, background): “In separate work, we have found that such measures for other models both stationary and non-stationary, and the work of R. L. Smith (1990, unpublished data), de Haan & Pereira (2006), Smith & Stephenson (2009) and Padoan et al. (2010) on the random storm formulation are also relevant.”
Conditional sampling for spectrally discrete max-stable random fields (2010, methodology): “Consistent and asymptotically normal estimators for the parameters ρ, β1, and β2 were obtained by de Haan and Pereira [12].”
An M‐estimator of spatial tail dependence (2014, background): “A ﬁrst example is de Haan and Pereira (2006), where several one-and two-dimensional models for spatial extremes are proposed.”
Likelihood-Based Inference for Max-Stable Processes (2009, methodology): “In accordance with spatial models, the extreme dependence between Z(0) and Z(h) decreases monotonically and continuously with h = ‖tj−ti‖ De Haan and Pereira (2006), and for fixed h the dependence decreases monotonically as a(h) increases.”