A study on the choice of the threshold in extreme value analyses

In the extreme value analyses based on the peaks-over-threshold method that underlie the determination of hydraulic boundary conditions informal procedures are used to choose the threshold. These procedures involve looking for threshold values around which the estimates of the shape parameter of the fitted distribution seem to be stable before becoming rather variable due to reduction of the sample size in an automatic way. There are, however, recently developed formal procedures for choosing the threshold which could prove to be more reliable. The purpose of this study is to investigate the possible gains that can be obtained from using formal methods instead of the informal ones in the context of determination of hydraulic boundary conditions. In order to assess the relative merits of a formal procedure described in Einmahl et al. (2009) and the ad hoc procedure currently used for the choice of the threshold in a peaks-overthreshold analysis, a simulation study was carried out. The procedures are compared in terms of their accuracy in estimating exceedance probabilities on the basis of time series with various lengths and with characteristics that mimic those of real time series.