Multivariate density estimation using dimension reducing information and tail flattening transformations

Insurance: Mathematics and Economics

Volumn 48, Issue 1, 2011, Pages 99-110

  Buch Kromann, Tine ^a   Guillén, Montserrat ^b   Linton, Oliver ^c   Nielsen, Jens Perch ^d  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

^b UNIVERSITY OF BARCELONA   (Spain)

^c LONDON SCHOOL OF ECONOMICS   (United Kingdom)

^d CITY UNIVERSITY   (United Kingdom)

Author keywords

Bias reduction; Kernel; Multiplicative correction

Indexed keywords

EID: 78649980073     PISSN: 01676687     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.insmatheco.2010.10.002     Document Type: Article

References (38)

1. Bolancé C., Guillén M., Nielsen J.P. Kernel density estimation of actuarial loss functions. Insurance: Mathematics and Economics 2003, 32:19-36.
2. Bolancé C., Guillén M., Nielsen J.P. Inverse beta transformation in kernel density estimation. Statistics and Probability Letters 2008, 78:1757-1764.
3. Bolancé C., Guillén M., Pelican E., Vernic R. Skewed bivariate models and nonparametric estimation for the CTE risk measure. Insurance: Mathematics and Economics 2008, 43(3):386-393.
4. Brodin E., Rootzén H. Univariate and bivariate GPD methods for predicting extreme wind storm losses. Insurance: Mathematics and Economics 2009, 44(3):345-356.
5. Buch-Kromann, T., 2009. Comparison of tail performance of the Champernowne transformed kernel density estimator, the generalized Pareto distribution and the g-and-h distribution.
6. Buch-Kromann T., Englund M., Gustafsson J., Nielsen J.P., Thuring F. Non-parametric estimation of operational risk losses adjusted for under-reporting. Scandinavian Actuarial Journal 2007, 4:293-304.
7. Buch-Larsen T., Nielsen J.P., Guillén M., Bolancé C. Kernel density estimation for heavy-tailed distributions using the Champernowne transformation. Statistics 2005, 39(6):503-518. 0233-1888.
8. Cao R., Vilar J.M., Devia A. Modelling consumer credit risk via survival analysis (with discussion). SORT 2009, 33(1):3-20.
9. Champernowne D.G. The graduation of income distributions. Econometrica 1952, 20:591-615.
10. Chen X., Linton O., Robinson P. The estimation of conditional densities. The Journal of Statistical Planning and Inference 2001, 71-84. (Special Issue in Honor of George Roussas.). 0020-3157.
11. Cherubini U., Mulinacci S., Romagnoli S. On the distribution of (un)bounded sum of random variables. Insurance: Mathematics and Economics 2010, Available online: 23 September 2010. 0167-6687, 10.1016/j.insmatheco.2010.09.004.
12. Clements A., Hurn S., Lindsay K. Mobius-like mappings and their use in kernel density estimation. Journal of the American Statistical Association 2003, 98(464):993-1000. 0162-1459.
13. Degen M., Embrechts P. EVT-based estimation of risk capital and cenvergence of high quantiles. Applied Probability Trust 2008, 3:696-715.
14. Degen M., Embrechts P., Lambrigger D.D. The quantitative modeling of operational risk: between g-and-h and EVT. Astin Bulletin 2007, 2(37):265-291.
15. Dutta, K., Perry, J., 2006. A tale of tails: an empirical analysis of loss distribution models for estimating operational risk capital. Federal Reserve Bank of Boston. Working Paper No. 06-13.
16. Furman E., Landsman Z. Multivariate Tweedie distributions and some related capital-at-risk analyses. Insurance: Mathematics and Economics 2010, 46(2):351-361.
17. Gebizlioglu O.L., Yagci B. Tolerance intervals for quantiles of bivariate risks and risk measurement. Insurance: Mathematics and Economics 2008, 42(3):1022-1027.
18. Genest C., Gerber H.U., Goovaerts M.J., Laeven R.J. Editorial to the special issue on modeling and measurement of multivariate risk in insurance and finance. Insurance: Mathematics and Economics 2009, 44(2):143-145.
19. Glad I.K., Hjort N.L., Ushakov N.G. Correction of density estimators that are not densities. Scandinavian Journal of Statistics 2003, 30(2):415-427. 0303-6898.
20. Guillén M., Gustafsson J., Nielsen J.P., Pritchard P. Using external data in operational risk. The Geneva Papers of Risk and Insurance-Issues and Practice 2007, 32(2):178-189.
21. Gustafsson J., Hagmann-von Arx M., Nielsen J.P., Scaillet O. Local transformation kernel density estimation of loss distributions. Journal of Business and Economic Statistics 2009, 27(2):1-15.
22. Gustafsson J., Nielsen J.P. A mixing model for operational risk. The Journal of Operational Risk 2008, 3(3):25-37.
23. Gustafsson J., Pritchard P., Nielsen J.P., Roberts D. Quantifying operational risk guided by kernel smoothing and continuous credibility: a practioner's view. The Journal of Operational Risk 2006, 1(1):43-55.
24. Hashorva E. Tail asymptotic results for elliptical distributions. Insurance: Mathematics and Economics 2008, 43(1):158-164.
25. Hjort N.L., Glad I.K. Nonparametric density estimation with a parametric start. The Annals of Statistics 1995, 23(3):882-904. 0090-5364.
26. Kallenberg W.C.M. Modelling dependence. Insurance: Mathematics and Economics 2008, 42(1):127-146.
27. Koekemoer G., Swanepoel J.W. Transformation kernel density estimation with applications. Journal of Computational and Graphical Statistics 2008, 17(3):750-769.
28. Li D., Peng L. Goodness-of-fit test for tail copulas modeled by elliptical copulas. Statistics and Probability Letters 2009, 79(8):1097-1104.
29. Linton O.B., Nielsen J.P., Nielsen S.F. Non-parametric regression with a latent time series. Econometrics Journal 2009, 12(2):187-212.
30. Phelps Brown E. Report of the Oxford meeting, September 25-29, 1936. Econometrica 1937, 5(4):361-383.
31. Scott D.W. Multivariate Density Estimation. Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics 1992, John Wiley & Sons Inc., New York, Theory, Practice, and Visualization, A Wiley-Interscience Publication. 0-471-54770-0.
32. Silverman B.W. Density Estimation for Statistics and Data Analysis. Monographs on Statistics and Applied Probability 1986, Chapman & Hall, London. 0-412-24620-1.
33. Stone C.J. Optimal rates of convergence for nonparametric estimators. The Annals of Statistics 1980, 8(6):1348-1360. 0090-5364.
34. Valdez E.A., Dhaene J., Maj M., Vanduffel S. Bounds and approximations for sums of dependent log-elliptical random variables. Insurance: Mathematics and Economics 2009, 44(3):385-397.
35. Vilar J.M., Cao R., González-Fragueiro C., Ausín M. Nonparametric analysis of aggregate loss models. Journal of Applied Statistics 2008, 36(2):149-166.
36. Wand M.P., Jones M.C. Kernel Smoothing 1995, vol. 60. Chapman and Hall Ltd., London, ISSN: 0-412-55270-1.
37. Wand M.P., Marron J.S., Ruppert D. Transformations in density estimation. Journal of the American Statistical Association 1991, 86(414):343-361. With discussion and a rejoinder by the authors. 0162-1459.
38. Yang L., Marron J.S. Iterated transformation-kernel density estimation. Journal of the American Statistical Association 1999, 94(446):580-589. 0162-1459.