Although the fundamental probabilistic theory of extremes has been well developed, there are many practical considerations that must be addressed in application. The contribution of this thesis is four-fold. The first concerns the choice of r in the r largest order statistics modeling of extremes. The second contribution pertains to threshold selection in the peaks-over-threshold approach. The third combines a theoretical and methodological approach to improve estimation within non-stationary regional frequency models of extremal data The methodology developed is demonstrated with climate based applications. Last, an overview of computational issues for extremes is provided, along with a brief tutorial of the R package eva, which improves the functionality of existing extreme value software, as well as providing new implementations.
Categories: stat.ME math.ST stat.AP stat.TH