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Scientific article
Open access
English

A Robust Prediction Error Criterion for Pareto Modeling of Upper Tails

Published inCanadian journal of statistics, vol. 34, no. 4, p. 639-358
Publication date2006
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
Citation (ISO format)
DUPUIS, Debbie, VICTORIA-FESER, Maria-Pia. A Robust Prediction Error Criterion for Pareto Modeling of Upper Tails. In: Canadian journal of statistics, 2006, vol. 34, n° 4, p. 639–358. doi: 10.1002/cjs.5550340406
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Article (Accepted version)
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Identifiers
ISSN of the journal0319-5724
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