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Beta kernel quantile estimators of heavy-tailed loss distributions

Author

Listed:
  • Arthur Charpentier

    (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique)

  • Abder Oulidi

    (MAI - Mathématiques Appliquées et Informatique - UCO - Université Catholique de l'Ouest)

Abstract

In this paper we suggest several nonparametric quantile estimators based on Beta kernel. They are applied to transformed data by the generalized Champernowne distribution initially fitted to the data. A Monte Carlo based study has shown that those estimators improve the efficiency of the traditional ones, not only for light tailed distributions, but also for heavy tailed, when the probability level is close to 1. We also compare these estimators with the Extreme Value Theory Quantile applied to Danish data on large fire insurance losses.

Suggested Citation

  • Arthur Charpentier & Abder Oulidi, 2010. "Beta kernel quantile estimators of heavy-tailed loss distributions," Post-Print halshs-00425566, HAL.
    • Handle: RePEc:hal:journl:halshs-00425566
    DOI: 10.1007/s11222-009-9114-2
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    Cited by:

    1. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    2. Charpentier, Arthur & Flachaire, Emmanuel, 2015. "Log-Transform Kernel Density Estimation Of Income Distribution," L'Actualité Economique, Société Canadienne de Science Economique, vol. 91(1-2), pages 141-159, Mars-Juin.
    3. Antoine J.‐P. Tixier & Matthew R. Hallowell & Balaji Rajagopalan, 2017. "Construction Safety Risk Modeling and Simulation," Risk Analysis, John Wiley & Sons, vol. 37(10), pages 1917-1935, October.
    4. Rocco Roberto Cerchiara & Francesco Acri, 2020. "Estimating the Volatility of Non-Life Premium Risk Under Solvency II: Discussion of Danish Fire Insurance Data," Risks, MDPI, vol. 8(3), pages 1-19, July.
    5. Hussein Khraibani & Bilal Nehme & Olivier Strauss, 2018. "Interval Estimation of Value-at-Risk Based on Nonparametric Models," Econometrics, MDPI, vol. 6(4), pages 1-30, December.
    6. Rocco Roberto Cerchiara & Francesco Acri, 2016. "Aggregate Loss Distribution And Dependence: Composite Models, Copula Functions And Fast Fourier Transform For The Danish Re Insurance Data," Working Papers 201608, Università della Calabria, Dipartimento di Economia, Statistica e Finanza "Giovanni Anania" - DESF.
    7. Yogendra P. Chaubey & Isha Dewan & Jun Li, 2021. "On Some Smooth Estimators of the Quantile Function for a Stationary Associated Process," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 114-139, May.

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