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

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  • 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. Practical application of the proposed estimator is illustrated with data from 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, Center for Open Science.
    • Handle: RePEc:osf:africa:hf7vk
    DOI: 10.31219/osf.io/hf7vk
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    References listed on IDEAS

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    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. 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.
    7. 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.
    8. 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.
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