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Bandwidth Selection for Multivariate Kernel Density Estimation Using MCMC

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  • Xibin Zhang
  • Maxwell L. King
  • Rob J. Hyndman

Abstract

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.

Suggested Citation

  • Xibin Zhang & Maxwell L. King & Rob J. Hyndman, 2004. "Bandwidth Selection for Multivariate Kernel Density Estimation Using MCMC," Monash Econometrics and Business Statistics Working Papers 9/04, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2004-9
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    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2004/wp9-04.pdf
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    References listed on IDEAS

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    1. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 361-393.
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    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, May.
    6. Tse, Y.K. & Zhang, Bill & Yu, Jun, 2002. "Estimation of Hyperbolic Diffusion using MCMC Method," Working Papers 182, Department of Economics, The University of Auckland.
    7. repec:bla:jfinan:v:53:y:1998:i:2:p:499-547 is not listed on IDEAS
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    Cited by:

    1. Zhang, Xibin & King, Maxwell L., 2008. "Box-Cox stochastic volatility models with heavy-tails and correlated errors," Journal of Empirical Finance, Elsevier, vol. 15(3), pages 549-566, June.
    2. Chauveau, Didier & Hoang, Vy Thuy Lynh, 2016. "Nonparametric mixture models with conditionally independent multivariate component densities," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 1-16.
    3. H. Poulos, 2010. "Spatially explicit mapping of hurricane risk in New England, USA using ArcGIS," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 54(3), pages 1015-1023, September.
    4. Kenneth L. Sørensen & Rune Vejlin, 2014. "Return To Experience And Initial Wage Level: Do Low Wage Workers Catch Up?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(6), pages 984-1006, September.

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    More about this item

    Keywords

    Bandwidth selection; cross-validation; multivariate kernel density estimation; sampling algorithms.;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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