Statistical inference and spatial modelling of extreme events

Specialeforsvar ved Alice Christine Raffenberg Ørnfelt

Titel: Statistical inference and spatial modelling of extreme events

 Abstract: Max-Stable processes are increasingly used in Extreme Value Theory applications, since they allow the spatial dependence of extremes to be modelled and quantified. We present an application to 15 years of daily maximum wind speed data in Denmark and study the maxima of multivariate processes with Fr´echet marginals using the Peaks Over Threshold approach. Based on limit theory of normalized and scaled maxima of stationary processes, we consider multivariate versions of five useful parametric Max-Stable models: the Smith, the Geometric Gaussian, the Brown-Resnick, the Schlather and the Extremal-t model. We describe pairwise likelihood estimation based on composite censored likelihoods, where the pairwise density of the process is used to estimate the model parameters and prove strong consistency and asymptotic normality of the parameter estimates for an increasing space dimension, i.e. as the spatial locations tends to infinity. A prediction study shows the expected behaviour of the wind at unobserved locations and a simulation study shows that the proposed method works well

Vejleder: Olivier Wintenberger
Censor:   Pierre Pinson, DTU