Local Transformation Kernel Density Estimation of Loss Distributions
AbstractWe develop a tailor made semiparametric asymmetric kernel density estimator for the estimation of actuarial loss distributions. The estimator is obtained by transforming the data with the generalized Champernowne distribution initially fitted to the data. Then the density of the transformed data is estimated by use of local asymmetric kernel methods to obtain superior estimation properties in the tails. We find in a vast simulation study that the proposed semiparametric estimation procedure performs well relative to alternative estimators. An application to operational loss data illustrates the proposed method.
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Bibliographic InfoPaper provided by Swiss Finance Institute in its series Swiss Finance Institute Research Paper Series with number 06-32.
Length: 32 pages
Date of creation: Nov 2006
Date of revision: Jun 2007
Actuarial loss models; Transformation; Champernowne distribution; asymmetric kernels; local likelihood estimation;
Other versions of this item:
- 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.
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
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- Hirukawa, Masayuki, 2010. "Nonparametric multiplicative bias correction for kernel-type density estimation on the unit interval," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 473-495, February.
- Buch-Kromann, Tine & Guillén, Montserrat & Linton, Oliver & Nielsen, Jens Perch, 2011. "Multivariate density estimation using dimension reducing information and tail flattening transformations," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 99-110, January.
- Hirukawa, Masayuki & Sakudo, Mari, 2014. "Nonnegative bias reduction methods for density estimation using asymmetric kernels," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 112-123.
- Nikolay Gospodinov & Masayuki Hirukawa, 2008. "Nonparametric Estimation of Scalar Diffusion Processes of Interest Rates Using Asymmetric Kernels," Working Papers 08011, Concordia University, Department of Economics, revised Dec 2008.
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