Short Course on The Empirical Process as a Tool in EVT Statistics

Asymptotically extreme order statistics (i.e. those with bounded upper rank number) are connected with a Poisson point process. This connection is sometimes a useful tool in proofs. For statistics of extreme values however one needs to use not only extreme but also intermediate order statistics (i.e. those with upper rank number tending to infinity but at a slower rate than the sample size). The asymptotics of intermediate order statistics is connected not with a point process but with a Brownian motion. This connection is quite useful as a tool in proofs of asymptotic normality of various statistics used in extreme value theory such as estimators for the extreme value index. I shall give an exposition of these approximation results and their use in EVT statistics.