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Estimation of the Tail Index of Pareto‐Type Distributions Using Regularisation

Author

Listed:
  • E. Ocran
  • R. Minkah
  • G. Kallah-Dagadu
  • K. Doku-Amponsah

Abstract

In this paper, we introduce reduced‐bias estimators for the estimation of the tail index of Pareto‐type distributions. This is achieved through the use of a regularised weighted least squares with an exponential regression model for log‐spacings of top‐order statistics. The asymptotic properties of the proposed estimators are investigated analytically and found to be asymptotically unbiased, asymptotically consistent, and asymptotically normally distributed. Also, the finite sample behaviour of the estimators are studied through a simulation study The proposed estimators were found to yield low bias and mean square errors. In addition, the proposed estimators are illustrated through the estimation of the tail index of the underlying distribution of claims from the insurance industry.

Suggested Citation

  • E. Ocran & R. Minkah & G. Kallah-Dagadu & K. Doku-Amponsah, 2022. "Estimation of the Tail Index of Pareto‐Type Distributions Using Regularisation," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:5064875
    DOI: 10.1155/2022/5064875
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    References listed on IDEAS

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    1. Gkillas, Konstantinos & Katsiampa, Paraskevi, 2018. "An application of extreme value theory to cryptocurrencies," Economics Letters, Elsevier, vol. 164(C), pages 109-111.
    2. Martin M. Kithinji & Peter N. Mwita & Ananda O. Kube, 2021. "Adjusted Extreme Conditional Quantile Autoregression with Application to Risk Measurement," Journal of Probability and Statistics, Hindawi, vol. 2021, pages 1-10, April.
    3. E. Ocran & R. Minkah & G. Kallah-Dagadu & K. Doku-Amponsah & Ljubisa Kocinac, 2022. "Estimation of the Tail Index of Pareto-Type Distributions Using Regularisation," Journal of Mathematics, Hindawi, vol. 2022, pages 1-16, October.
    4. E. Ocran & R. Minkah & G. Kallah-Dagadu & K. Doku-Amponsah, 2022. "Estimation of the Tail Index of Pareto‐Type Distributions Using Regularisation," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    5. Jan Beran & Dieter Schell & Milan Stehlík, 2014. "The harmonic moment tail index estimator: asymptotic distribution and robustness," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(1), pages 193-220, February.
    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.
    7. McNeil, Alexander J., 1997. "Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 117-137, May.
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    1. E. Ocran & R. Minkah & G. Kallah-Dagadu & K. Doku-Amponsah, 2022. "Estimation of the Tail Index of Pareto‐Type Distributions Using Regularisation," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).

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