A Folding Method for Extreme Quantiles Estimation

Abstract

In order to estimate extreme quantiles from independent and identically distributed random variables, we propose and study a novel folding procedure that improves quantile estimates obtained from the classical Peaks-Over-Threshold method (POT) used in Extreme Value Theory. The idea behind the folding approach is to connect the part of a distribution above a given threshold with the one below it. A simplified version of this approach was studied by You et al. (2010). In this paper, an extension based on two thresholds is proposed to better combine the folding scheme with the POT approach. Simulations indicate that this new strategy leads to improved extreme quantiles estimates for finite samples. Asymptotic normality of the folded POT estimators is also derived.

Keywords

• extreme quantile estimation
• peaks-over-thresholds
• generalized Pareto distribution
• folding
• generalized probability-weighted moments estimators