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Bandwidth Selection for Multivariate Kernel Density Estimation Using MCMC

  • Xibin Zhang

    ()

  • Maxwell L. King

    ()

  • Rob J. Hyndman

    ()

We provide Markov chain Monte Carlo (MCMC) algorithms for computing the bandwidth matrix for multivariate kernel density estimation. Our approach is based on treating the elements of the bandwidth matrix as parameters to be estimated, which we do by optimizing the likelihood cross-validation criterion. Numerical results show that the resulting bandwidths are superior to all existing methods; for dimensions greater than two, our algorithm is the first practical method for estimating the optimal bandwidth matrix. Moreover, the MCMC algorithm for bandwidth selection for multivariate data has no increased difficulty as the dimension of data increases.

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File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2004/wp9-04.pdf
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Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 9/04.

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Length: 25 pages
Date of creation: Apr 2004
Date of revision:
Handle: RePEc:msh:ebswps:2004-9
Contact details of provider: Postal: PO Box 11E, Monash University, Victoria 3800, Australia
Phone: +61-3-9905-2489
Fax: +61-3-9905-5474
Web page: http://www.buseco.monash.edu.au/depts/ebs/
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  1. BAUWENs, Luc & LUBRANO , Michel, 1996. "Bayesian Inference on GARCH Models using the Gibbs Sampler," CORE Discussion Papers 1996027, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Kim, Sangjoon & Shephard, Neil & Chib, Siddhartha, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Wiley Blackwell, vol. 65(3), pages 361-93, July.
  3. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
  4. Yacine Aït-Sahalia & Andrew W. Lo, 1998. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," Journal of Finance, American Finance Association, vol. 53(2), pages 499-547, 04.
  5. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew "t"-distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389.
  6. Y.K. Tse & Xibin Zhang & Jun Yu, 2002. "Estimation of Hyperbolic Diffusion Using MCMC Method," Monash Econometrics and Business Statistics Working Papers 18/02, Monash University, Department of Econometrics and Business Statistics.
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