Statistical inference for max-stable processes by conditioning on extreme events

Abstract

In this paper we provide the basis for new methods of inference for max-stable processes on general spaces that admit a certain incremental representation, which, in important cases, has a much simpler structure than the max-stable process itself. A corresponding peaks-over-threshold approach will incorporate all single events that are extreme in some sense and will therefore rely on a substantially larger amount of data in comparison to estimation procedures based on block maxima. Conditioning a process ? in the maxdomain of attraction of on being extremal, several convergence results for the increments of are proved. In a similar way, the shape functions of mixed moving maxima (M3) processes can be extracted from suitably conditioned single events ?. Connecting the two approaches, transformation formulae for processes that admit both an incremental and an M3 representation are identified. © Applied Probability Trust 2014.