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Local Transformation Kernel Density Estimation of Loss Distributions

Author

Listed:
  • J. Gustafsson

    (Codan Insurance and University of Copenhagen, Copenhagen, Denmark)

  • M. Hagmann

    (University of Geneva and Concordia Advisors, London, United Kingdom)

  • J.P. Nielsen

    (Festina Lente and University of Copenhagen, Copenhagen, Denmark)

  • O. Scaillet

    (University of Geneva and Swiss Finance Institute)

Abstract

We develop a tailor made semiparametric asymmetric kernel density estimator for the estimation of actuarial loss distributions. The estimator is obtained by transforming the data with the generalized Champernowne distribution initially fitted to the data. Then the density of the transformed data is estimated by use of local asymmetric kernel methods to obtain superior estimation properties in the tails. We find in a vast simulation study that the proposed semiparametric estimation procedure performs well relative to alternative estimators. An application to operational loss data illustrates the proposed method.

Suggested Citation

  • J. Gustafsson & M. Hagmann & J.P. Nielsen & O. Scaillet, 2006. "Local Transformation Kernel Density Estimation of Loss Distributions," Swiss Finance Institute Research Paper Series 06-32, Swiss Finance Institute, revised Jun 2007.
    • Handle: RePEc:chf:rpseri:rp0632
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    Cited by:

    1. Masayuki Hirukawa & Mari Sakudo, 2015. "Family of the generalised gamma kernels: a generator of asymmetric kernels for nonnegative data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(1), pages 41-63, March.
    2. Hirukawa, Masayuki & Sakudo, Mari, 2019. "Another bias correction for asymmetric kernel density estimation with a parametric start," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 158-165.
    3. Hirukawa, Masayuki, 2010. "Nonparametric multiplicative bias correction for kernel-type density estimation on the unit interval," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 473-495, February.
    4. Juxia Xiao & Xu Li & Jianhong Shi, 2019. "Local linear smoothers using inverse Gaussian regression," Statistical Papers, Springer, vol. 60(4), pages 1225-1253, August.
    5. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    6. Arthur Charpentier & Abder Oulidi, 2009. "Estimating allocations for Value-at-Risk portfolio optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(3), pages 395-410, July.
    7. Buch-Kromann, Tine & Guillén, Montserrat & Linton, Oliver & Nielsen, Jens Perch, 2011. "Multivariate density estimation using dimension reducing information and tail flattening transformations," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 99-110, January.
    8. Marcelo Fernandes & Eduardo Mendes & Olivier Scaillet, 2015. "Testing for symmetry and conditional symmetry using asymmetric kernels," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(4), pages 649-671, August.
    9. Gospodinov, Nikolay & Hirukawa, Masayuki, 2012. "Nonparametric estimation of scalar diffusion models of interest rates using asymmetric kernels," Journal of Empirical Finance, Elsevier, vol. 19(4), pages 595-609.
    10. Nikolay Gospodinov & Masayuki Hirukawa, 2008. "Nonparametric Estimation of Scalar Diffusion Processes of Interest Rates Using Asymmetric Kernels," Working Papers 08011, Concordia University, Department of Economics, revised Dec 2008.
    11. Song Li & Mervyn J. Silvapulle & Param Silvapulle & Xibin Zhang, 2015. "Bayesian Approaches to Nonparametric Estimation of Densities on the Unit Interval," Econometric Reviews, Taylor & Francis Journals, vol. 34(3), pages 394-412, March.
    12. María Luz Gámiz & Enno Mammen & María Dolores Martínez Miranda & Jens Perch Nielsen, 2016. "Double one-sided cross-validation of local linear hazards," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 755-779, September.
    13. Hirukawa, Masayuki & Sakudo, Mari, 2014. "Nonnegative bias reduction methods for density estimation using asymmetric kernels," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 112-123.
    14. F. R. B. Cruz & M. A. C. Santos & F. L. P. Oliveira & R. C. Quinino, 2021. "Estimation in a general bulk-arrival Markovian multi-server finite queue," Operational Research, Springer, vol. 21(1), pages 73-89, March.
    15. Karine Bertin & Nicolas Klutchnikoff, 2014. "Adaptive Estimation of a Density Function using Beta Kernels," Working Papers 2014-08, Center for Research in Economics and Statistics.

    More about this item

    Keywords

    Actuarial loss models; Transformation; Champernowne distribution; asymmetric kernels; local likelihood estimation;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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