Local asymptotic normality in {\delta}-neighborhoods of standard generalized Pareto processes

TL;DR

This paper extends the local asymptotic normality framework for spatial extremes to a functional setting, enabling efficient estimation of tail dependence parameters over a continuous spatial domain.

Contribution

It generalizes previous models by moving from finite point sets to continuous spatial parameter spaces in functional extreme value theory.

Findings

Derived efficient estimators for the tail dependence parameter {eta}.

Extended LAN results to functional processes in C[0,1].

Provided a framework for spatially continuous estimation in EVT.

Abstract

De Haan and Pereira (2006) provided models for spatial extremes in the case of stationarity, which depend on just one parameter {\beta} > 0 measuring tail dependence, and they proposed different estimators for this parameter. This framework was supplemented in 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. 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 in [a,b]. In particular, we derive efficient estimators of {\beta} based on those processes in a sample of iid processes in C[0,1] which exceed a given threshold function.