IDEAS home Printed from https://ideas.repec.org/p/osf/africa/hf7vk_v1.html
   My bibliography  Save this paper

Robust Extreme Quantile Estimation for Pareto-Type tails through an Exponential Regression Model

Author

Listed:
  • Minkah, Richard
  • de Wet, Tertius
  • Ghosh, Abhik

Abstract

The estimation of extreme quantiles is one of the main objectives of statistics of extremes ( which deals with the estimation of rare events). In this paper, a robust estimator of extreme quantile of a heavy-tailed distribution is considered. The estimator is obtained through the minimum density power divergence criterion on an exponential regression model. The proposed estimator was compared with two estimators of extreme quantiles in the literature in a simulation study. The results show that the proposed estimator is stable to the choice of the number of top order statistics and show lesser bias and mean square error compared to the existing extreme quantile estimators. Practical application of the proposed estimator is illustrated with data from the pedochemical and insurance industries.

Suggested Citation

  • Minkah, Richard & de Wet, Tertius & Ghosh, Abhik, 2022. "Robust Extreme Quantile Estimation for Pareto-Type tails through an Exponential Regression Model," AfricArxiv hf7vk_v1, Center for Open Science.
    • Handle: RePEc:osf:africa:hf7vk_v1
    DOI: 10.31219/osf.io/hf7vk_v1
    as

    Download full text from publisher

    File URL: https://osf.io/download/623a2c3f8d53ef08fb67de79/
    Download Restriction: no
    File URL: https://libkey.io/10.31219/osf.io/hf7vk_v1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Kim, Moosup & Lee, Sangyeol, 2008. "Estimation of a tail index based on minimum density power divergence," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2453-2471, November.
    2. L. de Haan, 1990. "Fighting the arch–enemy with mathematics‘," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 44(2), pages 45-68, June.
    3. Abhik Ghosh, 2017. "Divergence based robust estimation of the tail index through an exponential regression model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(2), pages 181-213, June.
    4. Dierckx, Goedele & Goegebeur, Yuri & Guillou, Armelle, 2013. "An asymptotically unbiased minimum density power divergence estimator for the Pareto-tail index," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 70-86.
    5. Manfred Gilli & Evis këllezi, 2006. "An Application of Extreme Value Theory for Measuring Financial Risk," Computational Economics, Springer;Society for Computational Economics, vol. 27(2), pages 207-228, May.
    6. M. Ivette Gomes & Laurens De Haan & Lígia Henriques Rodrigues, 2008. "Tail index estimation for heavy‐tailed models: accommodation of bias in weighted log‐excesses," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 31-52, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Minkah, Richard & de Wet, Tertius & Ghosh, Abhik, 2022. "Robust Extreme Quantile Estimation for Pareto-Type tails through an Exponential Regression Model," AfricArxiv hf7vk, Center for Open Science.
    2. Goegebeur, Yuri & Guillou, Armelle & Ho, Nguyen Khanh Le & Qin, Jing, 2020. "Robust nonparametric estimation of the conditional tail dependence coefficient," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    3. Dierckx, Goedele & Goegebeur, Yuri & Guillou, Armelle, 2013. "An asymptotically unbiased minimum density power divergence estimator for the Pareto-tail index," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 70-86.
    4. Goedele Dierckx & Yuri Goegebeur & Armelle Guillou, 2014. "Local robust and asymptotically unbiased estimation of conditional Pareto-type tails," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 330-355, June.
    5. Xiao Wang & Lihong Wang, 2024. "A tail index estimation for long memory processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(8), pages 947-971, November.
    6. Goedele Dierckx & Yuri Goegebeur & Armelle Guillou, 2021. "Local Robust Estimation of Pareto-Type Tails with Random Right Censoring," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 70-108, February.
    7. M. Ivette Gomes & Armelle Guillou, 2015. "Extreme Value Theory and Statistics of Univariate Extremes: A Review," International Statistical Review, International Statistical Institute, vol. 83(2), pages 263-292, August.
    8. Christophe Dutang & Yuri Goegebeur & Armelle Guillou, 2016. "Robust and Bias-Corrected Estimation of the Probability of Extreme Failure Sets," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(1), pages 52-86, February.
    9. Mikael Escobar-Bach & Yuri Goegebeur & Armelle Guillou & Alexandre You, 2017. "Bias-corrected and robust estimation of the bivariate stable tail dependence function," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 284-307, June.
    10. Christophe Dutang & Yuri Goegebeur & Armelle Guillou, 2016. "Robust and bias-corrected estimation of the probability of extreme failure sets," Post-Print hal-01616187, HAL.
    11. Goegebeur, Yuri & Guillou, Armelle & Verster, Andréhette, 2014. "Robust and asymptotically unbiased estimation of extreme quantiles for heavy tailed distributions," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 108-114.
    12. Yuri Goegebeur & Armelle Guillou & Théo Rietsch, 2015. "Robust conditional Weibull-type estimation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(3), pages 479-514, June.
    13. Moosup Kim & Sangyeol Lee, 2016. "On the tail index inference for heavy-tailed GARCH-type innovations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(2), pages 237-267, April.
    14. Fátima Brilhante, M. & Ivette Gomes, M. & Pestana, Dinis, 2013. "A simple generalisation of the Hill estimator," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 518-535.
    15. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    16. Carlin C. F. Chu & Simon S. W. Li, 2024. "A multiobjective optimization approach for threshold determination in extreme value analysis for financial time series," Computational Management Science, Springer, vol. 21(1), pages 1-14, June.
    17. 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.
    18. Maarten R C van Oordt & Chen Zhou, 2019. "Estimating Systematic Risk under Extremely Adverse Market Conditions," Journal of Financial Econometrics, Oxford University Press, vol. 17(3), pages 432-461.
    19. Gerlach, Richard & Wang, Chao, 2020. "Semi-parametric dynamic asymmetric Laplace models for tail risk forecasting, incorporating realized measures," International Journal of Forecasting, Elsevier, vol. 36(2), pages 489-506.
    20. M. Naresh Kumar & V. Sree Hari Rao, 2015. "A New Methodology for Estimating Internal Credit Risk and Bankruptcy Prediction under Basel II Regime," Computational Economics, Springer;Society for Computational Economics, vol. 46(1), pages 83-102, June.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:osf:africa:hf7vk_v1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: OSF (email available below). General contact details of provider: https://osf.io/preprints/africarxiv/discover .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.