Multivariate density estimation using dimension reducing information and tail flattening transformations
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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- 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.
- Bolance, Catalina & Guillen, Montserrat & Perch Nielsen, Jens, 2000. "Kernel Density Estimation of Actuarial Loss Functions," Finance Working Papers 00-4, University of Aarhus, Aarhus School of Business, Department of Business Studies.
- 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;The Geneva Association, vol. 32(2), pages 178-189, April.
- 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.
- Oliver Linton & Søren Feodor Nielsen & Jens Perch Nielsen, 2009. "Nonparametric Regression with a Latent Time Series," STICERD - Econometrics Paper Series 538, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Gustafsson, J. & Hagmann, M. & Nielsen, J. P. & Scaillet, O., 2009. "Local Transformation Kernel Density Estimation of Loss Distributions," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(2), pages 161-175.
- 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.
- Degen, Matthias & Embrechts, Paul & Lambrigger, Dominik D., 2007. "The Quantitative Modeling of Operational Risk: Between G-and-H and EVT," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 37(02), pages 265-291, November.
- 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.
- 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.
- 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.
- 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.
- Hashorva, Enkelejd, 2008. "Tail asymptotic results for elliptical distributions," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 158-164, August.
- 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.
- 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.
- 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.
- 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.
- 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. Full references (including those not matched with items on IDEAS)