Estimating extreme environmental variables by POT methods: behavior of Maximum Likelihood Estimators and distinction between statistical threshold and location parameter
Résumé
For a decade, the methodology for determining extreme values of environmental variables has converged towards the so-called GPD-Poisson model. The Peaks-Over-Threshold (POT) method is used for extracting extreme i.i.d. data from a time series. Excesses above a statistical meaningful threshold are fit to a 2-parameter Generalized Pareto Distribution (GPD), often with the Maximum Likelihood Estimator (MLE). Last, extreme values for desired return periods (quantiles) and confidence intervals are derived. In this approach, the GPD plays the role of an asymptotic approximation of the true law of excesses; hence it is valid when the threshold is high enough: a correct determination of the threshold value is thus crucial. Besides, a close examination of the sensitivity of the estimations with respect to the threshold shows that the use of 2-parameters (scale and shape) distributions yields unstable results. Considering the GPD (results are similar with other distributions), we explain in this presentation the need for a location parameter, distinct from the threshold, and the non-optimality of ML estimators.