Non-Stationary Dependence Structures for Spatial Extremes

Max-stable processes are natural models for spatial extremes because they provide suit-able asymptotic approximations to the distribution of maxima of random fields. In the recent past, several parametric families of stationary max-stable models have been devel-oped, 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 struc-tures 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 topogra-phy. Models are shown to satisfactorily capture extremal dependence