A flexible dependence model for spatial extremes

• Max-mixture combining max-stable and asymptotically independent spatial processes.
• Dependence, asymptotic independence and independence varying with inter-site distance.
• Statistical inference based on a composite likelihood approach.
• Rainfall data from a network of meteorological stations in South Eastern Australia.

Max-stable processes play a fundamental role in modeling the spatial dependence of extremes because they appear as a natural extension of multivariate extreme value distributions. In practice, a well-known restrictive assumption when using max-stable processes comes from the fact that the observed extremal dependence is assumed to be related to a particular max-stable dependence structure. As a consequence, the latter is imposed to all events which are more extreme than those that have been observed. Such an assumption is inappropriate in the case of asymptotic independence. Following recent advances in the literature, we exploit a max-mixture model to suggest a general spatial model which ensures extremal dependence at small distances, possible independence at large distances and asymptotic independence at intermediate distances. Parametric inference is carried out using a pairwise composite likelihood approach. Finally we apply our modeling framework to analyze daily precipitations over the East of Australia, using block maxima over the observation period and exceedances over a large threshold.