Extreme Region Likelihood Estimation

This lecture discusses the selection of an 'extreme' region A for likelihood estimation, focusing on the computation bottleneck and the use of pseudo-polar coordinates. Different choices of A lead to varying complexities in likelihoods, with simultaneous estimation of marginal and dependence features being preferred. The lecture also covers the modeling of oceanographic data using parametric distributions and the transformation of wave and surge height to unit Fréchet scale. Threshold likelihood estimation is explored, emphasizing the compromise between information loss and model stability. Nonparametric estimation and empirical likelihood approaches are also discussed, along with the implications of asymptotic theory and the estimation of marginal parameters.