Extreme Value Theory: Return Level Estimation

This lecture covers the motivation behind extremal limit theorems, the theory of maxima, point processes, Gaussian processes, and Poisson processes. It explores applications in multivariate extremes, statistics of multivariate extremes, and asymptotic independence models. The lecture delves into the estimation of return levels for extremes of time series, discussing consequences of clustering and declustering strategies. It also presents examples of rainfall data and various modelling strategies using exceedances and the Generalized Pareto Distribution (GPD). The lecture concludes with a summary of different estimators for the extremal index and strategies for return level estimation.