Local asymptotic normality in of standard generalized Pareto processes

De Haan and Pereira (2006) provided models for spatial extremes in the case of stationarity, which depend on just one parameter β > 0 measuring tail dependence, and they proposed different estimators for this parameter. This framework was supplemented by Falk (2011) by establishing local asymptotic normality (LAN) of a corresponding point process of exceedances above a high multivariate threshold, yielding in particular asymptotic efficient estimators. timators investigated in these papers are based on a finite set of points t 1 , … , t d , 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 t 1 , … , t d 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.