Kernel density estimation for heavy-tailed distributions using the champernowne transformation

Statistics

Volumn 39, Issue 6, 2005, Pages 503-516

  Buch Larsen, Tine ^a   Nielsen, Jens Perch ^b   Guillén, Montserrat ^c   Bolancé, Catalina ^c  

^a Department of Research ^*  (Denmark)

^b Royal and SunAlliance   (Denmark)

^c UNIVERSITY OF BARCELONA   (Spain)

Author keywords

Actuarial loss models; Champernowne distribution; Skewness; Transformation

Indexed keywords

EID: 30944439668     PISSN: 02331888     EISSN: 10294910     Source Type: Journal    
DOI: 10.1080/02331880500439782     Document Type: Article

References (22)

1. Wand, M.P. and Jones, M.C., 1995, Kernel Smoothing (London: Chapman & Hall).
2. Silverman, B.W., 1986, Density Estimation for Statistics and Data Analysis (London: Chapman & Hall).
3. Wand, P., Marron, J.S. and Ruppert, D., 1991, Transformations in density estimation. Journal of the American Statistical Association, 86, 343-361.
4. Bolancé, C., Guillén, M. and Nielsen, J.P., 2003, Kernel density estimation of actuarial loss functions. Insurance: Mathematics and Economics, 32, 19-36.
5. Yang, L. and Marron, J.S., 1999, Iterated transformation-kernel density estimation. Journal of the American Statistical Association, 94, 580-589.
6. Hjort, N.L. and Glad, I.K., 1995, Nonparametric density estimation with a parametric start. The Annals of Statistics, 23, 882-904.
7. Jones, M., Linton, O. and Nielsen, J.P., 1995, A simple bias reduction method for density estimaton. Biometrika, 82, 327-338.
8. Clements, A.E., Hum, 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.
9. Scaillet, O., 2004, Density estimation using inverse and reciprocal inverse Gaussian kernels. Journal of Nonparametric Statistics, 16, 217-226.
10. Johnson, N.L., Kotz, S. and Balakrishnan, N., 1994, Continuous Univariate Distributions, Vol. 1 (2nd edn) (New York: John Wiley & Sons).
11. Champernowne, D.G., 1936, The Oxford Meeting, September 25-29, Econometrica, 5, October 1937.
12. Champernowne, D.G., 1937, The theory of income distribution. Econometrica, 5, 379-381.
13. Champernowne D.G., 1952, The graduation of income distributions. Econometrica, 20, 591-615.
14. Coles, S., 2001, An Introduction to Statistical Modelling of Extreme Values (Berlin: Springer).
15. Lehmann, E.L., 1983, Theory of Point Estimation (New York: Wiley).
16. Tukey, J.W., 1960, A survey of sampling from comtaminated distributions. In: I. Olkin (Ed.) Contributions to Probability and Statistics (Stanford, California: Standford University Press).
17. Stigler, S.M., 1973, Simon Newcomb, Percy Daniell, and the history of robust estimation. Journal of the American Statistical Association, 68, 872-879.
18. Newcomb, S., 1882, Discussion and results of observations on transits of Mercury from 1677 to 1881. Astronomical Papers, 1, 363-487.
19. Newcomb, S., 1886, A generalized theory of the combination of observations so as to obtain the best results. American Journal of Mathematics, 8, 343-366.
20. Hubert, P.J., 1981, Robust Statistics (New York: John Wiley & Sons).
21. Yang, L., 2000, Root-n convergent transformation-kernel density estimation. Journal of Nonparametric Statistics, 12, 447-474.
22. Sheather, S.J. and Jones, M.C., 1991, A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society, Series B, 53, 683-690.