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Bandwidth Selection for Multivariate Kernel Density Estimation Using MCMC

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Author Info
Xibin Zhang ()
Maxwell L. King ()
Rob J. Hyndman ()

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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.

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File URL: http://www.buseco.monash.edu.au/depts/ebs/pubs/wpapers/2004/wp9-04.pdf
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Publisher Info
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
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Handle: RePEc:msh:ebswps:2004-9

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Related research
Keywords: Bandwidth selection; cross-validation; multivariate kernel density estimation; sampling algorithms.;

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Find related papers by JEL classification:
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Bayesian Analysis
C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Luc Bauwens & Michel Lubrano, 1998. "Bayesian inference on GARCH models using the Gibbs sampler," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages C23-C46.
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  2. Yacine Ait-Sahalia & Andrew W. Lo, 1995. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," NBER Working Papers 5351, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  3. Kim, Sangjoon & Shephard, Neil & Chib, Siddhartha, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Blackwell Publishing, vol. 65(3), pages 361-93, July. [Downloadable!] (restricted)
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  4. 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. [Downloadable!] (restricted)
  5. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 9(2), pages 385-426. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Xibin Zhang & Maxwell L. King, 2004. "Box-Cox Stochastic Volatility Models with Heavy-Tails and Correlated Errors," Monash Econometrics and Business Statistics Working Papers 26/04, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
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