Statistics Department Seminar Series: Stilian Stoev, Associate Professor, Department of Statistics, University of Michigan

Suppose that one measures precipitation at several synoptic stations over  multiple days. We say that we have concurrence of extremes if the maximum  precipitation over time is achieved simultaneously at all stations, e.g., on a single day. This is a strong indication of spatial dependence where a single "storm event" causes the extremes. Under general conditions, the finite  sample concurrence probability converges to an asymptotic quantity, deemed  extremal concurrence probability. This was first established in Hashorva and  Hüsler (2005) (see also Stephenson and Tawn (2005) and Wadsworth and  Tawn (2015)). Using Palm calculus, we establish general expressions for the  extremal concurrence probability through the max-stable process emerging in  the limit of the component-wise maxima of the sample. Explicit forms of the  extremal concurrence probabilities are obtained for various max-stable models and several estimators are introduced. In particular, we prove that the  pairwise extremal concurrence probability for max-stable vectors equals the Kendall's tau. The estimators are evaluated by using simulations and applied to study the expected area of concurrence regions of temperature extremes in the United States. The results demonstrate that  concurrence probability can provide a new perspective and tools for the analysis of the spatial structure and impact of extremes. (Joint work with Clément Dombry and Mathieu Ribatet).