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A Modified Quantile Estimator Using Extreme-Value Theory with Applications

Author

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  • Vermaat M. B.
  • Does R. J. M. M.

    (Institute for Business and Industrial Statistics, IBIS UvA, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands)

  • Steerneman A. G. M.

    (Department of Econometrics, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands)

Abstract

Reliable predictions by means of quantiles constitute one of the most important tasks not only in statistics but in entire science. Quantiles may be estimated by using Extreme- Value Theory (EVT). However, the properties of many estimators based on this theory depend heavily on the actual location. In this paper modified estimators for the quantiles are derived, the properties of which are less sensitive with respect to location. Moreover, these modified quantile estimators are also symmetric with regard to the mean for symmetric distributions, which is not the case for some of the estimators based on the EVT. The modified quantile estimators are a limiting result of an infinity shift of location of the estimators proposed by Dekkers et al. (The Annals of Statistics 17: 1833–1855, 1989). The results may be used in establishing control limits for Shewhart control charts.

Suggested Citation

  • Vermaat M. B. & Does R. J. M. M. & Steerneman A. G. M., 2005. "A Modified Quantile Estimator Using Extreme-Value Theory with Applications," Stochastics and Quality Control, De Gruyter, vol. 20(1), pages 31-39, January.
    • Handle: RePEc:bpj:ecqcon:v:20:y:2005:i:1:p:31-39:n:5
    DOI: 10.1515/EQC.2005.31
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    References listed on IDEAS

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    1. Einmahl, J. H.J. & Dekkers, A. L.M. & de Haan, L., 1989. "A moment estimator for the index of an extreme-value distribution," Other publications TiSEM 81970cb3-5b7a-4cad-9bf6-2, Tilburg University, School of Economics and Management.
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    Cited by:

    1. Mohamed El Ghourabi & Amira Dridi & Mohamed Limam, 2015. "A new financial stress index model based on support vector regression and control chart," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(4), pages 775-788, April.
    2. Imed Gammoudi & Lotfi BelKacem & Mohamed El Ghourabi, 2014. "Value at Risk Estimation for Heavy Tailed Distributions," The International Journal of Business and Finance Research, The Institute for Business and Finance Research, vol. 8(3), pages 109-125.
    3. Amira Dridi & Mohamed El Ghourabi & Mohamed Limam, 2012. "On monitoring financial stress index with extreme value theory," Quantitative Finance, Taylor & Francis Journals, vol. 12(3), pages 329-339, March.

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