Title: 
Threshold selection for modeling exceedances
over high thresholds

Authors:
Philippe Naveau
Department of Applied Mathematics, 
Colorado University at Boulder, USA and
Institut Pierre Simon Laplace, LSCE, France
naveau@colorado.edu

Uli Schneider
Geophysical Statistics Project.
National Center for Atmospheric Research, USA.
schneider@ucar.edu

Abstract:
The statistical modeling of extreme events is in most cases based on 
the study of exceedances above a high threshold. The Generalized Pareto distribution (GPD) usually 
provides an adequate model for such exceedances, whenever the number of observations and 
the threshold are large enough. 
But, even in the iid case, the choice of the threshold remains difficult.
Although Frigessi and al. (2003) and Dupuis (1999) have recently proposed two new  but complex ways of 
addressing this question, this research also showed  that 
 the need for easy-to-implement and general procedures for fitting the GPD with an appropriate threshold 
 is still of importance.
 In this talk, we propose a novel and simple method to improve the estimation of the GPD coefficients 
 and to reduce the uncertainties of those parameters.
 Our method is based on a folding procedure that allows us to bypass the trade-off linked to the 
threshold selection; the latter has to
be high enough to justify the GDP fit but low enough to capture 
 a reasonable number of exceedances. 
The main idea of our approach is to transform all the data set  in order that
the modified observations all belong to the tail of the distribution, i.e. above a high threshold.
The description of this folding transformation as well as the study of its properties are the main focus of this talk.
 This new procedure is  tested on a variety of simulated data and 
 illustrated by examples stemming from climate research.