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Detecting influential data points for the Hill estimator in Pareto-type distributions

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  • Hubert, Mia
  • Dierckx, Goedele
  • Vanpaemel, Dina

Abstract

Pareto-type distributions are extreme value distributions for which the extreme value index γ>0. Classical estimators for γ>0, like the Hill estimator, tend to overestimate this parameter in the presence of outliers. The empirical influence function plot, which displays the influence that each data point has on the Hill estimator, is introduced. To avoid a masking effect, the empirical influence function is based on a new robust GLM estimator for γ. This robust GLM estimator is used to determine high quantiles of the data generating distribution, allowing to flag data points as unusually large if they exceed this high quantile.

Suggested Citation

  • Hubert, Mia & Dierckx, Goedele & Vanpaemel, Dina, 2013. "Detecting influential data points for the Hill estimator in Pareto-type distributions," Computational Statistics & Data Analysis, Elsevier, vol. 65(C), pages 13-28.
    • Handle: RePEc:eee:csdana:v:65:y:2013:i:c:p:13-28
    DOI: 10.1016/j.csda.2012.07.011
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    1. Armelle Guillou & Peter Hall, 2001. "A diagnostic for selecting the threshold in extreme value analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 293-305.
    2. Rosario Dell’Aquila & Paul Embrechts, 2006. "Extremes and Robustness: A Contradiction?," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 20(1), pages 103-118, April.
    3. Debruyne, Michiel & Hubert, Mia & Van Horebeek, Johan, 2010. "Detecting influential observations in Kernel PCA," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3007-3019, December.
    4. Hubert, M. & Vandervieren, E., 2008. "An adjusted boxplot for skewed distributions," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5186-5201, August.
    5. Drees, Holger & Kaufmann, Edgar, 1998. "Selecting the optimal sample fraction in univariate extreme value estimation," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 149-172, July.
    6. Pison, Greet & Rousseeuw, Peter J. & Filzmoser, Peter & Croux, Christophe, 2003. "Robust factor analysis," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 145-172, January.
    7. Cai, J. & Einmahl, J.H.J. & de Haan, L.F.M., 2011. "Estimation of extreme risk regions under multivariate regular variation," Other publications TiSEM b7a72a8d-f9bc-4129-ae9b-a, Tilburg University, School of Economics and Management.
    8. Vytaras Brazauskas & Robert Serfling, 2000. "Robust and Efficient Estimation of the Tail Index of a Single-Parameter Pareto Distribution," North American Actuarial Journal, Taylor & Francis Journals, vol. 4(4), pages 12-27.
    9. Cantoni, Eva & Ronchetti, Elvezio, 2006. "A robust approach for skewed and heavy-tailed outcomes in the analysis of health care expenditures," Journal of Health Economics, Elsevier, vol. 25(2), pages 198-213, March.
    10. Cantoni E. & Ronchetti E., 2001. "Robust Inference for Generalized Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1022-1030, September.
    11. Vandewalle, B. & Beirlant, J. & Christmann, A. & Hubert, M., 2007. "A robust estimator for the tail index of Pareto-type distributions," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6252-6268, August.
    12. McElroy, Tucker & Jach, Agnieszka, 2012. "Tail index estimation in the presence of long-memory dynamics," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 266-282.
    13. Cédric Perret-Gentil & Maria-Pia Victoria-Feser, 2005. "Robust Mean-Variance Portfolio Selection," FAME Research Paper Series rp140, International Center for Financial Asset Management and Engineering.
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    Cited by:

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    2. Gareth W. Peters & Matteo Malavasi & Georgy Sofronov & Pavel V. Shevchenko & Stefan Trück & Jiwook Jang, 2023. "Cyber loss model risk translates to premium mispricing and risk sensitivity," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 48(2), pages 372-433, April.
    3. Arthur Charpentier & Emmanuel Flachaire, 2019. "Pareto Models for Top Incomes," Working Papers hal-02145024, HAL.
    4. Gareth W. Peters & Matteo Malavasi & Georgy Sofronov & Pavel V. Shevchenko & Stefan Truck & Jiwook Jang, 2022. "Cyber Loss Model Risk Translates to Premium Mispricing and Risk Sensitivity," Papers 2202.10588, arXiv.org, revised Mar 2023.
    5. Asimit, Alexandru V. & Badescu, Alexandru M. & Verdonck, Tim, 2013. "Optimal risk transfer under quantile-based risk measurers," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 252-265.
    6. Nasir Abbas & Mu’azu Ramat Abujiya & Muhammad Riaz & Tahir Mahmood, 2020. "Cumulative Sum Chart Modeled under the Presence of Outliers," Mathematics, MDPI, vol. 8(2), pages 1-30, February.
    7. Yuri Goegebeur & Armelle Guillou & Jing Qin, 2023. "Robust estimation of the conditional stable tail dependence function," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(2), pages 201-231, April.

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