Séance Séminaire

Séminaire de Probabilités et Statistique

Spatial extremes with a single realization: a geostatistical point of view.

Spatial extreme value theory helps model and predict the frequency of extreme events in a spatial context like, for instance, extreme precipitations, extreme temperatures. It is well adapted to time series. However, in some cases, such types of data cannot be accessed: only one or just a few records are made available. This is the case, for instance in soil contamination evaluation. This situation is rarely addressed in the spatial extremes community, contrary to Geostatistics, which typically deals with such issues. The aim of our work is to make some connections between both disciplines, in order to better handle the study of spatial extreme events, and especially their spatial dependence structure, when having only one set of spatial observations. A link is first established through the concept of integral range. It is a geostatistical parameter that characterizes the statistical fluctuations of a stationary random field at large scale. When the latter is max-stable, we show that its extremal coefficient function (ECF), which is a measure of spatial dependence, is closely related to the integral range of the corresponding exceedance field above a threshold. From this, we move to proposing a new nonparametric estimator of the ECF. Its asymptotic properties are derived when it is computed from a single and partially observed realization of a stationary max-stable random field. Specifically, under some assumptions on the aforementioned integral range, we prove that it is consistent and asymptotically normal.

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