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Inverse beta transformation in kernel density estimation

Author

Listed:
  • Bolancé, Catalina
  • Guillén, Montserrat
  • Nielsen, Jens Perch

Abstract

A transformation kernel density estimator that is suitable for heavy-tailed distributions is presented. Using a double transformation, the choice of the bandwidth parameter becomes straightforward. An illustration and simulation results are presented.

Suggested Citation

  • Bolancé, Catalina & Guillén, Montserrat & Nielsen, Jens Perch, 2008. "Inverse beta transformation in kernel density estimation," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1757-1764, September.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:13:p:1757-1764
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    References listed on IDEAS

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    1. Bolance, Catalina & Guillen, Montserrat & Nielsen, Jens Perch, 2003. "Kernel density estimation of actuarial loss functions," Insurance: Mathematics and Economics, Elsevier, vol. 32(1), pages 19-36, February.
    2. Wu, Tiee-Jian & Chen, Ching-Fu & Chen, Huang-Yu, 2007. "A variable bandwidth selector in multivariate kernel density estimation," Statistics & Probability Letters, Elsevier, vol. 77(4), pages 462-467, February.
    3. Clements A. & Hurn S. & Lindsay K., 2003. "Mobius-Like Mappings and Their Use in Kernel Density Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 993-1000, January.
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    Citations

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    Cited by:

    1. Catalina Bolance & Montserrat Guillen & David Pitt, 2014. "Non-parametric Models for Univariate Claim Severity Distributions - an approach using R," Working Papers 2014-01, Universitat de Barcelona, UB Riskcenter.
    2. Bolancé, Catalina & Bahraoui, Zuhair & Artís, Manuel, 2014. "Quantifying the risk using copulae with nonparametric marginals," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 46-56.
    3. Ramon Alemany & Catalina Bolancé & Montserrat Guillén, 2012. "Nonparametric estimation of Value-at-Risk," Working Papers XREAP2012-19, Xarxa de Referència en Economia Aplicada (XREAP), revised Oct 2012.
    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. 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.
    6. David Pitt & Montserrat Guillén, 2010. "An introduction to parametric and non-parametric models for bivariate positive insurance claim severity distributions," Working Papers XREAP2010-03, Xarxa de Referència en Economia Aplicada (XREAP), revised Mar 2010.
    7. David Pitt & Montserrat Guillen & Catalina Bolancé, 2011. "Estimation of Parametric and Nonparametric Models for Univariate Claim Severity Distributions - an approach using R," Working Papers XREAP2011-06, Xarxa de Referència en Economia Aplicada (XREAP), revised Jun 2011.
    8. Catalina Bolancé & Montserrat Guillen, 2021. "Nonparametric Estimation of Extreme Quantiles with an Application to Longevity Risk," Risks, MDPI, vol. 9(4), pages 1-23, April.
    9. Bolance, Catalina & Guillen, Montserrat & Pelican, Elena & Vernic, Raluca, 2008. "Skewed bivariate models and nonparametric estimation for the CTE risk measure," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 386-393, December.
    10. Nagler, Thomas & Czado, Claudia, 2016. "Evading the curse of dimensionality in nonparametric density estimation with simplified vine copulas," Journal of Multivariate Analysis, Elsevier, vol. 151(C), pages 69-89.
    11. Alemany, Ramon & Bolancé, Catalina & Guillén, Montserrat, 2013. "A nonparametric approach to calculating value-at-risk," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 255-262.
    12. Tine Buch-Kromann & Jens Nielsen, 2012. "Multivariate density estimation using dimension reducing information and tail flattening transformations for truncated or censored data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(1), pages 167-192, February.
    13. Derennes, Pierre & Morio, Jérôme & Simatos, Florian, 2019. "A nonparametric importance sampling estimator for moment independent importance measures," Reliability Engineering and System Safety, Elsevier, vol. 187(C), pages 3-16.
    14. J. M. Vilar & R. Cao & M. C. Ausin & C. Gonzalez-Fragueiro, 2009. "Nonparametric analysis of aggregate loss models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(2), pages 149-166.
    15. Ramon Alemany & Catalina Bolance & Montserrat Guillen, 2014. "Accounting for severity of risk when pricing insurance products," Working Papers 2014-05, Universitat de Barcelona, UB Riskcenter.
    16. Jeon, Yongho & Kim, Joseph H.T., 2013. "A gamma kernel density estimation for insurance loss data," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 569-579.
    17. Ramon ALEMANY & Catalina BOLANCÉ & Montserrat GUILLÉN & Alemar E. PADILLA-BARRETO, 2016. "Combining Parametric And Non-Parametric Methods To Compute Value-At-Risk," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 50(4), pages 61-74.

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