Estimation of Hüsler–Reiss distributions and Brown–Resnick processes

By Sebastian Engelke, Alexander Malinowski, Zakhar Kabluchko, Martin Schlather. 2012

152 citations recorded by the source corpus.

Estimation of extreme value parameters from observations in the max‐domain of attraction of a multivariate max‐stable distribution commonly uses aggregated data such as block maxima. Multivariate peaks‐over‐threshold methods, in contrast, exploit additional information from the non‐aggregated ‘large’ observations. We introduce an approach based on peaks over thresholds that provides several new estimators for processes η in the max‐domain of attraction of the frequently used Hüsler–Reiss model and its spatial extension: Brown–Resnick processes. The method relies on increments η(·)−η(t0) conditional on η(t0) exceeding a high threshold, where t0 is a fixed location. When the marginals are standardized to the Gumbel distribution, these increments asymptotically form a Gaussian process resulting in computationally simple estimates of the Hüsler–Reiss parameter matrix and particularly enables parametric inference for Brown–Resnick processes based on (high dimensional) multivariate densities. This is a major advantage over composite likelihood methods that are commonly used in spatial extreme value statistics since they rely only on bivariate densities. A simulation study compares the performance of the new estimators with other commonly used methods. As an application, we fit a non‐isotropic Brown–Resnick process to the extremes of 12‐year data of daily wind speed measurements.

Subfields: Economics and Econometrics, Finance, Health, Toxicology and Mutagenesis

View Paper: https://www.semanticscholar.org/paper/2855f6a88a44c2721696e02ee8b6c324497777ab

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Citations in the corpus

Efficient inference and simulation for elliptical Pareto processes (2013, methodology): “In their treatment of estimation procedures for the Brown–Resnick process, Engelke et al. (2012) propose using `(f) = ∑D j=1 f(sj), leading to the multivariate sum spectral measure, or `(f) = f(s0) for some fixed site s0, leading to the notion of extremal increments.”
Geostatistics of Dependent and Asymptotically Independent Extremes (2013, methodology): “…based on the full likelihood have been proposed for a special class of max-stable processes that includes the Brown–Resnick processes (Wadsworth and Tawn 2013), and Engelke et al. (2012) proposed to fit Brown– Resnick processes based on the full likelihood of extremal increments of the process.”
Non-Stationary Dependence Structures for Spatial Extremes (2014, methodology): “…tool for inference in this context (Padoan et al., 2010; Thibaud et al., 2013; Huser and Davison, 2014), although more efficient approaches based on the point process characterization of extremes have recently been proposed (Wadsworth and Tawn, 2014; Thibaud and Opitz, 2014; Engelke et al., 2014).”
Modeling asymptotically independent spatial extremes based on Laplace random fields (2015, unknown): “Recent studies on similar data (Engelke et al., 2015; Einmahl et al., 2015; Oesting et al., 2015) are based on max-stable models without challenging the assumption of asymptotic dependence.”
Extremes on river networks (2015, methodology): “As also noted by Engelke et al. (2015) and Einmahl et al. (2015), the estimates of λEuc have larger variation than the others.”
Bridging asymptotic independence and dependence in spatial extremes using Gaussian scale mixtures (2016, unknown): “Alternatively, models for threshold exceedances based on the limiting Poisson (Wadsworth and Tawn, 2014; Engelke et al., 2015) or the generalized Pareto (Ferreira and de Haan, 2014; Thibaud and Opitz, 2015) process are the counter-parts of max-stable models for threshold exceedances and have become…”
Functional peaks‐over‐threshold analysis (2020, background): “Identifiability issues that may arise with the parametric models for A and B can be solved for instance by ensuring that r(A) = 1, and, for a linear functional, r(B) = 0; see Engelke et al. (2019), for example.”
An M‐estimator of spatial tail dependence (2014, methodology): “Comparison with Engelke et al. (2014). To compare the pairwise M-estimator with the one from Engelke et al. (2014), we consider the setting used in the simulation study of the latter paper: we simulate 500 samples of size 8000 of the univariate Brown–Resnick process on an equidistant grid on the int”
Modeling Spatial Processes with Unknown Extremal Dependence Class (2017, background): “…exceedances, which have simpler likelihoods, have become more appealing; see, for example, Ferreira and deHaan (2014),Wadsworth and Tawn (2014), Engelke et al. (2015), Thibaud and Opitz (2015), and de Fondeville and CONTACT Jennifer Wadsworth j.wadsworth@lancaster.ac.uk Department of…”