Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.14/132556
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- Title
- A Bayesian approach to parameter estimation for kernel density estimation via transformations
- Related
- Annals of actuarial science, Vol. 5, Issue 2, (2011), p.181-193
- DOI
- 10.1017/S1748499511000030
- Publisher
- Cambridge University Press
- Date
- 2011
- FoR/RFCD Code(s)
-
150200 Banking, Finance and Investment
010200 Applied Mathematics
- Author/Creator
- Liu, Qing
- Author/Creator
- Pitt, David
- Author/Creator
- Zhang, Xibin
- Author/Creator
- Wu, Xueyuan
- Description
- Published online: 18 April 2011. In this paper, we present a Markov chain Monte Carlo (MCMC) simulation algorithm for estimating parameters in the kernel density estimation of bivariate insurance claim data via transformations. Our data set consists of two types of auto insurance claim costs and exhibits a high-level of skewness in the marginal empirical distributions. Therefore, the kernel density estimator based on original data does not perform well. However, the density of the original data can be estimated through estimating the density of the transformed data using kernels. It is well known that the performance of a kernel density estimator is mainly determined by the bandwidth, and only in a minor way by the kernel. In the current literature, there have been some developments in the area of estimating densities based on transformed data, where bandwidth selection usually depends on pre-determined transformation parameters. Moreover, in the bivariate situation, the transformation parameters were estimated for each dimension individually. We use a Bayesian sampling algorithm and present a Metropolis-Hastings sampling procedure to sample the bandwidth and transformation parameters from their posterior density. Our contribution is to estimate the bandwidths and transformation parameters simultaneously within a Metropolis-Hastings sampling procedure. Moreover, we demonstrate that the correlation between the two dimensions is better captured through the bivariate density estimator based on transformed data.
- Description
- 13 page(s)
- Subject Keyword
- 150200 Banking, Finance and Investment
- Subject Keyword
- 010200 Applied Mathematics
- Subject Keyword
- bandwidth Parameter
- Subject Keyword
- kernel density estimator
- Subject Keyword
- Markov Chain Monte Carlo
- Subject Keyword
- Metropolis-Hastings Algorithm
- Subject Keyword
- power transformation
- Subject Keyword
- transformation parameter
- Resource Type
- journal article
- Organisation
- Macquarie University. Dept. of Applied Finance and Actuarial Studies
- Identifier
- http://hdl.handle.net/1959.14/132556
- Identifier
- ISSN:1748-4995
- Identifier
- mq-rm-2010005290
- Language
- eng
- Full Text
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