A Robust Prediction Error Criterion for Pareto Modeling of Upper Tails

Canadian Journal of Statistics, Vol. 34, No. 4, pp. 639-358, 2006

21 Pages Posted: 12 Feb 2011

Date Written: July 23, 2006

Abstract

Estimation of the Pareto tail index from extreme order statistics is an important problem in many settings. The upper tail of the distribution, where data are sparse, is typically fitted with a model, such as the Pareto model, from which quantities such as probabilities associated with extreme events are deduced. The success of this procedure relies heavily not only on the choice of the estimator for the Pareto tail index but also on the procedure used to determine the number k of extreme order statistics that are used for the estimation. The authors develop a robust prediction error criterion to choose k and estimate the Pareto index. A simulation study shows the good performance of the new estimator and the analysis of real data sets shows that a robust procedure for selection, and not just for estimation, is needed.

Keywords: Extreme values, tail index, income distribution, value at risk, M-estimators, regression

Suggested Citation

Dupuis, Debbie and Victoria-Feser, Maria-Pia, A Robust Prediction Error Criterion for Pareto Modeling of Upper Tails (July 23, 2006). Canadian Journal of Statistics, Vol. 34, No. 4, pp. 639-358, 2006, Available at SSRN: https://ssrn.com/abstract=1760027

Debbie Dupuis

HEC Montreal ( email )

3000, Chemin de la Côte-Sainte-Catherine
Montreal, Quebec H2X 2L3
Canada

Maria-Pia Victoria-Feser (Contact Author)

University of Geneva - HEC ( email )

40 Boulevard du Pont d'Arve
Geneva 4, Geneva 1211
Switzerland

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