Local transformation kernel density estimation of loss distributions

Journal of Business and Economic Statistics

Volumn 27, Issue 2, 2009, Pages 161-175

  Gustafsson, J ^a   Hagmann, M ^b   Nielsen, J P ^c   Scaillet, O ^b  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

^b SWISS FINANCE INSTITUTE   (Switzerland)

^c CITY UNIVERSITY   (United Kingdom)

Author keywords

Actuarial loss models; Asymmetric kernels; Champernowne distribution; Local likelihood estimation; Transformation

Indexed keywords

EID: 70350564101     PISSN: 07350015     EISSN: None     Source Type: Journal    
DOI: 10.1198/jbes.2009.0011     Document Type: Article

References (36)

1. Banks, J., Blundell, R., and Lewbel, A. (1997), "Quadratic Engel Curves and Consumer Demand," The Review of Economics and Statistics, 79, 527-539. (Pubitemid 128002659)
2. Bolance, C., Guillen, M., and Nielsen, J. P. (2003), "Kernel Density Estimation of Actuarial Loss Functions," Insurance, Mathematics & Economics, 32, 19-36. (Pubitemid 36136281)
3. Bouezmarni, T., and Rolin, J. M. (2004), "Consistency of Beta Kernel Density Function Estimator," The Canadian Journal of Statistics, 31, 89-98.
4. Bouezmarni, T., and Scaillet, O. (2005), "Consistency of Asymmetric Kernel Density Estimators and Smoothed Histograms with Application to Income Data," Econometric Theory, 21, 390-412. (Pubitemid 40551428)
5. Brown, B. M., and Chen, S. X. (1999), "Beta-Bernstein Smoothing for Regression Curves with Compact Supports," Scandinavian Journal of Statistics, 26, 47-59.
6. Buch-Larsen, T., Nielsen, J. P., Guillen, M., and Bolance, C. (2005), "Kernel Density Estimation for Heavy-tailed Distributions Using the Champernowne Transformation," Statistics, 39, 503-518. (Pubitemid 43109067)
7. Champernowne, D. G. (1936), "The Oxford Meeting, September 25-29, 1936," Econometrica, 5, [October 1937], 361-383.
8. - (1952), "The Graduation of Income Distributions," Econometrica, 20, 591-615.
9. Chen, S. X. (1999), "A Beta Kernel Estimator for Density Functions," Computational Statistics & Data Analysis, 31, 131-145.
10. - (2000), "Probability Density Function Estimation Using Gamma Kernels," Annals of the Institute of Statistical Mathematics, 52, 471-480.
11. Clements, A. E., Hurn, A. S., and Lindsay, K. A. (2003), "Möbius-like Mappings and Their Use in Kernel Density Estimation," Journal of the American Statistical Association, 98, 993-1000. (Pubitemid 38213989)
12. Diebold, F. X., Gunther, H., and Tay, C. (1998), "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, 39, 863-883.
13. Fan, J., and Gijbels, I. (1992), "Variable Bandwidth and Local Linear Regression Smoothers," The Annals of Statistics, 20, 2008-2036.
14. Gouriéroux, C., Monfort, A., and Trognon, A. (1984), "Pseudo Maximum Likelihood Methods: Theory," Econometrica, 52, 680-700.
15. Gustafsson, J., Nielsen, J. P., Pritchard, P., and Roberts, D., (2006), "Quantifying Operational Risk Guided by Kernel Smoothing and Continuous Credibility: A Practioner's View," The Journal of Operational Risk, 1 (1), 43-56.
16. Gustafsson, J., and Thuring, F. (2006). "Best Distribution for Severity Modelling: A Computational Evaluation of Different Loss Distribution Assumptions," Working Paper.
17. Hagmann, M., and Scaillet, O. (2007), "Local Multiplicative Bias Correction for Asymmetric Kernel Density Estimators," Journal of Econometrics, 141, 213-249. (Pubitemid 47419179)
18. Hjort, N. L., and Glad, I. K. (1995), "Nonparametric Density Estimation with a Parametric Start," The Annals of Statistics, 24, 882-904.
19. Hjort, N. L., and Jones, M. C. (1996), "Locally Parametric Nonparametric Density Estimation," The Annals of Statistics, 24, 1619-1647. (Pubitemid 127007696)
20. Hogg, R., and Klugman, S. A. (1984). Loss Distributions, New York: John Wiley & Sons, Inc.
21. Härdle, W., and Linton, O. (1994). "Applied Nonparametric Methods. Handbook of Econometrics IV, " (eds) R. Engle and D. McFadden, Amsterdam: North-Holland, 2295-2339.
22. Jones, M. C. (1993), "Simple Boundary Correction for Kernel Density Estimation," Statistics and Computing, 3, 135-146.
23. Jones, M. C., and Foster, P. (1996), "A Simple Nonnegative Boundary Correction Method for Kernel Density Estimation," Statistica Sinica, 6, 1005-1013. (Pubitemid 127004421)
24. Klugman, S. A., Panjer, H. A., and Willmot, G. E. (1998). Loss Models: From Data to Decisions, New York: John Wiley & Sons, Inc.
25. Lehmann, E. L. (1991). Theory of Point Estimation, Belmont, CA: Wadsworth & Brooks/Cole.
26. Müller, H. (1991), "Smooth Optimum Kernel Estimators near Endpoints," Biometrika, 78, 521-530.
27. Pagan, A., and Ullah, A. (1999). Nonparametric Econometrics, New York; Cambridge, UK: Cambridge University Press.
28. Renault, O., and Scaillet, O. (2004), "On the Way to Recovery: A Non-parametric Bias Free Estimation of Recovery Rate Densities," Journal of Banking & Finance, 28, 2915-2931. (Pubitemid 39407465)
29. Rice, J. (1984), "Boundary Modification for Kernel Regression," Communications in Statistics Theory and Methods, 13, 893-900.
30. Rosenblatt, M. (1956),"Remarks on Some Nonparametric Estimates of a Density Function," Annals of Mathematical Statistics, 27, 642-669.
31. Scaillet, O. (2004), "Density Estimation Using Inverse and Reciprocal Inverse Gaussian Kernels," Journal of Nonparametric Statistics, 16, 217-226. (Pubitemid 38178265)
32. Schuster, E. (1985), "Incorporating Support Constraints into Nonparametric Estimators of Densities," Communications in Statistics Theory and Methods, 14, 1123-1136.
33. Silverman, B. W. (1986). Density Estimation for Statistics and Data Analysis, London. Chapman & Hall.
34. Wand, M. P., and Jones, M. C. (1995). Kernel Smoothing, New York: Chapman & Hall.
35. Wand, M. P., Marron, J. S., and Ruppert, D. (1991), "Transformation in Density Estimation (with comments)," Journal of the American Statistical Association, 94, 1231-1241.
36. White, H. (1982), "Maximum Likelihood Estimation of Misspecified Models," Econometrica, 50, 1-26.