227981
20190509132609.0
10.5075/epfl-thesis-7479
doi
urn:nbn:ch:bel-epfl-thesis7479-5
urn
10894038
nebis
THESIS
eng
7479
Contributions to Modelling Extremes of Spatial Data
Lausanne
2017
EPFL
2017
217
Theses
Prof. Victor Panaretos (président) ; Prof. Anthony C. Davison (directeur de thèse) ; Prof. Stephan Morgenthaler, Prof. Valérie Chavez-Demoulin, Dr Marc-Olivier Boldi (rapporteurs)
The 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.
Brown--Resnick process
Composite likelihood
Conditionally negative definite matrix
Degenerate distribution
Hüsler--Reiss model
Karhunen--Loève expansion
Max-stable process
r-largest order statistics model
Total ozone data
Frossard, Linda
170781
244568
Davison, Anthony C.
dir.
111184
240476
n/a
34889825
n/a
http://infoscience.epfl.ch/record/227981/files/EPFL_TH7479.pdf
STAT
252136
U10124
oai:infoscience.tind.io:227981
SB
DOI
thesis-bn2018
thesis
GLOBAL_SET
DOI2
108898
108898
SB
MATHAA
EDMA
STAT
2017-5-10
2017
7479/THESES
EPFL
PUBLISHED
THESIS