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Bandwidth Selection for Multivariate Kernel Density Estimation Using MCMC

Author

Listed:
  • Rob L. Hyndman
  • Xibin Zhang
  • Maxwell L. King,
Abstract
Kernel density estimation for multivariate data is an important technique that has a wide range of applications in econometrics and finance. However, it has received significantly less attention than its univariate counterpart. The lower level of interest in multivariate kernel density estimation is mainly due to the increased difficulty in deriving an optimal data-driven bandwidth as the dimension of data increases. We provide Markov chain Monte Carlo (MCMC) algorithms for estimating optimal bandwidth matrices for multivariate kernel density estimation. Our approach is based on treating the elements of the bandwidth matrix as parameters whose posterior density can be obtained through the likelihood cross-validation criterion. Numerical studies for bivariate data show that the MCMC algorithm generally performs better than the plug-in algorithm under the Kullback-Leibler information criterion, and is as good as the plug-in algorithm under the mean integrated squared errors (MISE) criterion. Numerical studies for 5 dimensional data show that our algorithm is superior to the normal reference rule. Our MCMC algorithm is the first data-driven bandwidth selector for kernel density estimation with more than two variables, and the sampling algorithm involves no increased difficulty as the dimension of data increase

Suggested Citation

  • Rob L. Hyndman & Xibin Zhang & Maxwell L. King,, 2004. "Bandwidth Selection for Multivariate Kernel Density Estimation Using MCMC," Econometric Society 2004 Australasian Meetings 120, Econometric Society.
    • Handle: RePEc:ecm:ausm04:120
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    File URL: http://repec.org/esAUSM04/up.1603.1077410300.pdf
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    References listed on IDEAS

    as
    1. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," The Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
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    5. Stephen G. Donald, 1997. "Inference Concerning the Number of Factors in a Multivariate Nonparametric Relationship," Econometrica, Econometric Society, vol. 65(1), pages 103-132, January.
    6. repec:bla:jfinan:v:53:y:1998:i:2:p:499-547 is not listed on IDEAS
    7. 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.
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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 matrices; Cross-validation; Kullback-Leibler information; mean integrated squared errors; Sampling algorithms.;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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