000227981 001__ 227981
000227981 005__ 20190509132609.0
000227981 0247_ $$2doi$$a10.5075/epfl-thesis-7479
000227981 02470 $$2urn$$aurn:nbn:ch:bel-epfl-thesis7479-5
000227981 02471 $$2nebis$$a10894038
000227981 037__ $$aTHESIS
000227981 041__ $$aeng
000227981 088__ $$a7479
000227981 245__ $$aContributions to Modelling Extremes of Spatial Data
000227981 260__ $$bEPFL$$c2017$$aLausanne
000227981 269__ $$a2017
000227981 300__ $$a217
000227981 336__ $$aTheses
000227981 502__ $$aProf. Victor Panaretos (président) ; Prof. Anthony C. Davison (directeur de thèse) ; Prof. Stephan Morgenthaler, Prof. Valérie Chavez-Demoulin, Dr Marc-Olivier Boldi (rapporteurs)
000227981 520__ $$aThe increasing interest in using statistical extreme value theory to analyse environmental data is mainly driven by the large impact extreme events can have. A difficulty with spatial data is that most existing inference methods for asymptotically justified models for extremes are computationally intractable for data at several hundreds of sites, a number easily attained or surpassed by the output of physical climate models or satellite-based data sets. This thesis does not directly tackle this problem, but it provides some elements that might be useful in doing so. The first part of the thesis contains a pointwise marginal analysis of satellite-based measurements of total column ozone in the northern and southern mid-latitudes. At each grid cell, the r-largest order statistics method is used to analyse extremely low and high values of total ozone, and an autoregressive moving average time series model is used for an analogous analysis of mean values. Both models include the same set of global covariates describing the dynamical and chemical state of the atmosphere. The results show that influence of the covariates is captured in both the ``bulk'' and the tails of the statistical distribution of ozone. For some covariates, our results are in good agreement with findings of earlier studies, whereas unprecedented influences are retrieved for two dynamical covariates. The second part concerns the frameworks of multivariate and spatial modelling of extremes. We review one class of multivariate extreme value distributions, the so-called Hüsler--Reiss model, as well as its spatial extension, the Brown--Resnick process. For the former, we provide a detailed discussion of its parameter matrix, including the case of degeneracy, which arises if the correlation matrices of underlying multivariate Gaussian distributions are singular. We establish a simplification for computing the partial derivatives of the exponent function of these two models. As consequence of the considerably reduced number of terms in each partial derivative, computation time for the multivariate joint density of these models can be reduced, which could be helpful for (composite) likelihood inference. Finally, we propose a new variant of the Brown--Resnick process based on the Karhunen--Loève expansion of its underlying Gaussian process. As an illustration, we use composite likelihood to fit a simplified version of our model to a hindcast data set of wave heights that shows highly dependent extremes.
000227981 6531_ $$aBrown--Resnick process
000227981 6531_ $$aComposite likelihood
000227981 6531_ $$aConditionally negative definite matrix
000227981 6531_ $$aDegenerate distribution
000227981 6531_ $$aHüsler--Reiss model
000227981 6531_ $$aKarhunen--Loève expansion
000227981 6531_ $$aMax-stable process
000227981 6531_ $$ar-largest order statistics model
000227981 6531_ $$aTotal ozone data
000227981 700__ $$0244568$$g170781$$aFrossard, Linda
000227981 720_2 $$aDavison, Anthony C.$$edir.$$g111184$$0240476
000227981 8564_ $$uhttps://infoscience.epfl.ch/record/227981/files/EPFL_TH7479.pdf$$zn/a$$s34889825$$yn/a
000227981 909C0 $$xU10124$$0252136$$pSTAT
000227981 909CO $$pthesis-bn2018$$pDOI$$pSB$$ooai:infoscience.tind.io:227981$$qDOI2$$qGLOBAL_SET$$pthesis
000227981 917Z8 $$x108898
000227981 917Z8 $$x108898
000227981 918__ $$dEDMA$$cMATHAA$$aSB
000227981 919__ $$aSTAT
000227981 920__ $$b2017$$a2017-5-10
000227981 970__ $$a7479/THESES
000227981 973__ $$sPUBLISHED$$aEPFL
000227981 980__ $$aTHESIS