In many applications (geosciences, insurance,...), the Peaks‐Over‐Thresholds (POT) approach is one of the most widely used methodology for extreme quantile inference. It mainly consists of approximating the distribution of exceedances above a high threshold by a Generalized Pareto Distribution (GPD). The number of exceedances which is used in the POT inference is often quite small and this leads typically to a high volatility of the estimates. Inspired by perfect sampling techniques used in simulation studies, we propose a folding procedure that connects the lower and upper parts of a distribution. A new extreme quantile estimator motivated by this theoretical folding scheme is proposed and studied. This is illustrated our approach with simulation studies in an univariate and multivariate context.
Joint work with A. You, A. Guillou and U. Schneider