On the use of the peaks over thresholds method for estimating out-of-sample quantiles

• Authors: Mhamed-Ali El-Aroui;Jean Diebolt
• Venue: Computational Statistics & Data Analysis
• Year: 2002

The peaks over thresholds (POT) method used to estimate out-of-sample quantiles is considered. The investigation concerns of how well this method can estimate quantiles beyond the largest available observation. The problem of measuring precision of extreme quantiles estimations (for finite samples) is discussed. Intensive Monte Carlo experiments are used to assess the quality of POT estimations. Effects of the several POT parameters and tuning are analyzed and optimal levels are given. The extrapolation ability of POT is modeled using available covariates with Discriminant Analysis and Generalized Linear Models. This provides a simulation-based user's guide predicting for each data-set which extreme quantiles can be well estimated, i.e. how far from the largest observation it is possible to get precise quantile estimation. Warranties, warnings and empirical confidence intervals (in a nonasymptotic context) are given to practitioners using POT to estimate out-of-sample quantiles