×

Inverse beta transformation in kernel density estimation. (English) Zbl 1147.62323

Summary: A transformation kernel density estimator that is suitable for heavy-tailed distributions is presented. Using a double transformation, the choice of the bandwidth parameter becomes straightforward. An illustration and simulation results are presented.

MSC:

62G07 Density estimation
62G32 Statistics of extreme values; tail inference
65C60 Computational problems in statistics (MSC2010)

Software:

KernSmooth
PDFBibTeX XMLCite
Full Text: DOI HAL

References:

[1] Bolancé, C.; Guillén, M.; Nielsen, J. P., Kernel density estimation of actuarial loss functions, Insurance: Mathematics and Economics, 32, 19-36 (2003) · Zbl 1024.62041
[2] Buch-Larsen, T.; Guillen, M.; Nielsen, J. P.; Bolancé, C., Kernel density estimation for heavy-tailed distributions using the Champernowne transformation, Statistics, 39, 503-518 (2005) · Zbl 1095.62040
[3] Clements, A. E.; Hurn, A. S.; Lindsay, K. A., Mö bius-like mappings and their use in kernel density estimation, Journal of the American Statistical Association, 98, 993-1000 (2003) · Zbl 1045.62023
[4] Jones, M. C., Variable kernel density estimation and variable kernel density estimation, Australian Journal of Statistics, 32, 361-371 (1990)
[5] Johnson, N. L.; Jotz, S.; Balakrishnan, N., Continuous Univariate Distributions, vol. 1 (1995), John Wiley & Sons, Inc.: John Wiley & Sons, Inc. New York · Zbl 0821.62001
[6] Silverman, B. W., Density Estimation for Statistics and Data Analysis (1986), Chapman & Hall: Chapman & Hall London · Zbl 0617.62042
[7] Terrell, G. R., The maximal smoothing principle in density estimation, Journal of the American Statistical Association, 85, 270-277 (1990)
[8] Terrell, G. R.; Scott, D. W., Oversmoothed nonparametric density estimates, Journal of the American Statistical Association, 80, 209-214 (1985)
[9] Wand, M. P.; Jones, M. C., Kernel Smoothing (1995), Chapman & Hall: Chapman & Hall London · Zbl 0854.62043
[10] Wand, P.; Marron, J. S.; Ruppert, D., Transformations in density estimation, Journal of the American Statistical Association, 86, 414, 343-361 (1991) · Zbl 0742.62046
[11] Wu, T.-J.; Chen, C.-F.; Chen, H.-Y., A variable bandwidth selector in multivariate kernel density estimation, Statistics & Probability Letters, 77, 462-467 (2007) · Zbl 1108.62037
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.