About
Risk assessment for extremes of natural phenomena has become increasingly important, and over the past few years the scientific community has realized the importance of considering the spatial or spatio-temporal extent of extreme events. The extreme-value distributions play an important role in the statistical modeling of extremes at individual locations, but for risk assessment it is crucial to assess dependence between extremes at locations: if dependence is strong, rare events might occur simultaneously at many different locations, thereby increasing the overall risk.
In this thesis, new dependence models for space-time extremes, based on asymptotically justified arguments, are developed, and novel inference methods for fitting these models to observations exceeding high thresholds are proposed. The approach advocated is more efficient than traditional methods based on block (typically annual) maxima, and enables more detailed analysis of extremes, but requires a more sophisticated treatment of dependence.
The ideas are illustrated by application to hourly rainfall data from western Switzerland, and prove to be satisfactory for realistic modeling of their extremal properties.
