Local asymptotic normality in δ-neighborhoods of standard generalized Pareto processes

The estimators investigated in these papers are based on a finite set of points t1,…,td, at which observations are taken. We generalize this approach in the context of functional extreme value theory (EVT). This more general framework allows estimation over some spatial parameter space, i.e., the finite set of points t1,…,td is replaced by t∈[a,b]. In particular, we derive efficient estimators of β based on those processes in a sample of iid processes in C[0,1] which exceed a given threshold function.