Likelihood-based inference for max-stable processes

The last decade has seen max-stable processes emerge as a common tool for the statistical modeling of spatial extremes. However, their application is complicated due to the unavailability of the multivariate density function, and so likelihood-based methods remain far from providing a complete and flexible framework for inference. In this article we develop inferentially practical, likelihood-based methods for fitting max-stable processes derived from a composite-likelihood approach. The procedure is sufficiently reliable and versatile to permit the simultaneous modeling of marginal and dependence parameters in the spatial context at a moderate computational cost. The utility of this methodology is examined via simulation, and illustrated by the analysis of U.S. precipitation extremes

Models for extremal dependence derived from skew-symmetric families

Skew-symmetric families of distributions such as the skew-normal and skew-$t$ represent supersets of the normal and $t$ distributions, and they exhibit richer classes of extremal behaviour. By defining a non-stationary skew-normal process, which allows the easy handling of positive definite, non-stationary covariance functions, we derive a new family of max-stable processes - the extremal-skew-$t$ process. This process is a superset of non-stationary processes that include the stationary extremal-$t$ processes. We provide the spectral representation and the resulting angular densities of the extremal-skew-$t$ process, and illustrate its practical implementation (Includes Supporting Information).Comment: To appear in Scandinavian Journal of Statistic