A Prediction Error Criterion for Choosing the Lower Quantile in Pareto Index Estimation

• Activity Number: 27
• Type: Contributed
• Date/Time: Sunday, August 3, 2003 : 2:00 PM to 3:50 PM
• Sponsor: General Methodology
• Author(s): Maria-Pia Victoria-Feser*+ and Debbie J. Dupuis
• Companies: University of Geneva and University of Western Ontario
• Keywords: tail index ; mean excess function ; goodness-of-fit ; extreme value distributions

Abstract

The success of estimation of the Pareto tail index from extreme order statistics relies heavily on the procedure used to determine their number. Most of the procedures are based on the minimization of (an estimate of) the asymptotic mean square error of the Hill estimator for the Pareto tail index. The principal drawback of these approaches is that they involve the estimation of nuisance parameters, and therefore can lead to complicated selection procedures. Instead, we propose to use Pareto quantile plots, as defined in Beirlant et al. (1996) for example, and build a prediction error estimator. The latter depends on the quantile at which the data are truncated, and it is minimized to find the optimal number of extreme order statistics. The main advantages of the new approach are computational simplicity and the absence of estimation of nuisance parameters. The prediction error estimator is actually a generalization of Mallows' C_{p} to non-normal regression models. Through a simulation study involving several data generating models, we show that our prediction error criterion performs very well in terms of MSE compared to other procedures.