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Multivariate density estimation using dimension reducing information and tail flattening transformations

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Author Info

  • Buch-Kromann, Tine
  • Guillén, Montserrat
  • Linton, Oliver
  • Nielsen, Jens Perch

Abstract

We propose a nonparametric multiplicative bias corrected transformation estimator designed for heavy tailed data. The multiplicative correction is based on prior knowledge and has a dimension reducing effect at the same time as the original dimension of the estimation problem is retained. Adding a tail flattening transformation improves the estimation significantly-particularly in the tail-and provides significant graphical advantages by allowing the density estimation to be visualized in a simple way. The combined method is demonstrated on a fire insurance data set and in a data-driven simulation study.

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Bibliographic Info

Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

Volume (Year): 48 (2011)
Issue (Month): 1 (January)
Pages: 99-110

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Handle: RePEc:eee:insuma:v:48:y:2011:i:1:p:99-110

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Web page: http://www.elsevier.com/locate/inca/505554

Related research

Keywords: Bias reduction Kernel Multiplicative correction;

References

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  1. Montserrat Guillen & Jim Gustafsson & Jens Perch Nielsen & Paul Pritchard, 2007. "Using External Data in Operational Risk," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan, vol. 32(2), pages 178-189, April.
  2. Kabir Dutta & Jason Perry, 2006. "A tale of tails: an empirical analysis of loss distribution models for estimating operational risk capital," Working Papers 06-13, Federal Reserve Bank of Boston.
  3. Brodin, Erik & Rootzén, Holger, 2009. "Univariate and bivariate GPD methods for predicting extreme wind storm losses," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 345-356, June.
  4. Ingrid K. Glad, 2003. "Correction of Density Estimators that are not Densities," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 30(2), pages 415-427.
  5. 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.
  6. 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.
  7. Li, Deyuan & Peng, Liang, 2009. "Goodness-of-fit test for tail copulas modeled by elliptical copulas," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1097-1104, April.
  8. Genest, Christian & Gerber, Hans U. & Goovaerts, Marc J. & Laeven, Roger J.A., 2009. "Editorial to the special issue on modeling and measurement of multivariate risk in insurance and finance," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 143-145, April.
  9. Oliver Linton & Jens Perch Nielsen & Søren Feodor Nielsen, 2009. "Non-parametric regression with a latent time series," Econometrics Journal, Royal Economic Society, vol. 12(2), pages 187-207, 07.
  10. Xiaohong Chen & Oliver Linton & Peter M Robinson, 2001. "The Estimation of Conditional Densities," STICERD - Econometrics Paper Series /2001/415, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  11. 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.
  12. Hashorva, Enkelejd, 2008. "Tail asymptotic results for elliptical distributions," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 158-164, August.
  13. Gebizlioglu, Omer L. & Yagci, Banu, 2008. "Tolerance intervals for quantiles of bivariate risks and risk measurement," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1022-1027, June.
  14. Furman, Edward & Landsman, Zinoviy, 2010. "Multivariate Tweedie distributions and some related capital-at-risk analyses," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 351-361, April.
  15. 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.
  16. 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.
  17. Valdez, Emiliano A. & Dhaene, Jan & Maj, Mateusz & Vanduffel, Steven, 2009. "Bounds and approximations for sums of dependent log-elliptical random variables," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 385-397, June.
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Citations

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Cited by:
  1. 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.
  2. Del Brio, Esther B. & Perote, Javier, 2012. "Gram–Charlier densities: Maximum likelihood versus the method of moments," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 531-537.

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