Automated, Efficient, and Practical Extreme Value Analysis with Environmental Applications

Abstract

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.