Geostatistics of Dependent and Asymptotically Independent Extremes

Davison, A. C.; Huser, Raphaël; Thibaud, Emeric

doi:10.1007/s11004-013-9469-y

Cited by 92 publications

(76 citation statements)

References 73 publications

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“…For more details about univariate and multivariate extremes, see Beirlant et al (2004) and Davison and Huser (2015), and for an account of spatial extremes, see the review papers 5 by , Cooley et al (2012) and Davison et al (2013). See also the book by de Haan and Ferreira (2006), which explains the technicalities in depth.…”

Section: Theoretical Foundationmentioning

confidence: 99%

Non-Stationary Dependence Structures for Spatial Extremes

Huser

Genton

2016

JABES

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Max-stable processes are natural models for spatial extremes because they provide suitable asymptotic approximations to the distribution of maxima of random fields. In the recent past, several parametric families of stationary max-stable models have been developed, and fitted to various types of data. However, a recurrent problem is the modeling of non-stationarity. In this paper, we develop non-stationary max-stable dependence structures in which covariates can be easily incorporated. Inference is performed using pairwise likelihoods, and its performance is assessed by an extensive simulation study based on a non-stationary locally isotropic extremal t model. Evidence that unknown parameters are well estimated is provided, and estimation of spatial return level curves is discussed. The methodology is demonstrated with temperature maxima recorded over a complex topography. Models are shown to satisfactorily capture extremal dependence.

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Section: Theoretical Foundationmentioning

confidence: 99%

Non-Stationary Dependence Structures for Spatial Extremes

Huser

Genton

2016

JABES

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“…This paper can be regarded as a practical guide when fitting annual maxima of precipitation data. This work contrasts with existing comparisons of spatial extreme value methods as in Davison et al (2012) or Davison et al (2013) in two ways: on the one hand, it is the first study, as far as we know, that includes the hierarchical model of Reich and Shaby (2012); on the other hand, the use of simulated data that are tailored on real precipitation data enables the comparison to be more objective.…”

Section: General Conclusionmentioning

confidence: 99%

“…The latter model has not been considered in the present paper because of its unrealistic over smooth feature and a resulting lack of fit on real data. See for instance Davison et al (2012) or Davison et al (2013), where the Gaussian extreme value model is compared with the EGP and the BRP, among others.…”

Section: The Hierarchical Kernel Extreme Value Process: Hkevpmentioning

confidence: 99%

Modeling extreme rainfall A comparative study of spatial extreme value models

2017

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In this paper, focus is done on spatial models for extreme events and on their respective efficiency regarding the estimation of two risk measures: one extrapolating marginal distributions and one summarizing the spatial bivariate dependence of extremes. A wide comparison is performed on an innovative simulation plan that has been specifically designed from a daily precipitation data set. The objective of this paper is twofold: firstly, pointing out the inherent properties of each model, and secondly, advising users on how to choose the model depending on the specific type of risk.

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“…In the analysis of multivariate data, it is often difficult to make a choice between AD and AI; see, e.g., [3], [11] and [18]. By having a model that has both AD and AI components, we can avoid having to make this key decision.…”

Section: Introductionmentioning

confidence: 99%

“…For this model it can be shown thatχ = 1 and χ = 2 − m i=1 max(α i , β i ), so the variables are AD. On exponential margins, simulations from the max-linear model in (3) give lines of mass, parallel with X E = Y E , and points scattered around these lines, as shown on Figure 1a, where X E and Y E were determined by X F = max(0.7Z 1 , 0.2Z 2 , 0.1Z 3 ) and Y F = max(0.4Z 1 , 0.5Z 2 , 0.1Z 4 ). The number of Z i variables in common between X F and Y F determines the number of lines with mass on.…”

Section: Introductionmentioning

confidence: 99%

Properties of extremal dependence models built on bivariate max-linearity

Kereszturi

Tawn

2017

Journal of Multivariate Analysis

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Please cite this article as: M. Kereszturi, J. Tawn, Properties of extremal dependence models built on bivariate max-linearity, Journal of Multivariate Analysis (2016), http://dx.doi.org/10. 1016/j.jmva.2016.12.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Properties of extremal dependence models built on bivariate max-linearityMónika Kereszturi * and Jonathan Tawn STOR-i Centre for Doctoral Training, Lancaster University, UK AbstractBivariate max-linear models provide a core building block for characterizing bivariate max-stable distributions. The limiting distribution of marginally normalized component-wise maxima of bivariate max-linear models can be dependent (asymptotically dependent) or independent (asymptotically independent). However, for modeling bivariate extremes they have weaknesses in that they are exactly max-stable with no penultimate form of convergence to asymptotic dependence, and asymptotic independence arises if and only if the bivariate max-linear model is independent. In this work we present more realistic structures for describing bivariate extremes. We show that these models are built on bivariate max-linearity but are much more general. In particular, we present models that are dependent but asymptotically independent and others that are asymptotically dependent but have penultimate forms. We characterize the limiting behavior of these models using two new different angular measures in a radial-angular representation that reveal more structure than existing measures.

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Geostatistics of Dependent and Asymptotically Independent Extremes

Cited by 92 publications

References 73 publications

Non-Stationary Dependence Structures for Spatial Extremes

Non-Stationary Dependence Structures for Spatial Extremes

Modeling extreme rainfall A comparative study of spatial extreme value models

Properties of extremal dependence models built on bivariate max-linearity

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