Bandwidth Selection for Multivariate Kernel Density Estimation Using MCMC

Rob Hyndman, Xibin Zhang and Maxwell King

No 120, Econometric Society 2004 Australasian Meetings from Econometric Society

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

Keywords: Bandwidth matrices; Cross-validation; Kullback-Leibler information; mean integrated squared errors; Sampling algorithms. (search for similar items in EconPapers)
JEL-codes: C11 C14 C15 (search for similar items in EconPapers)
Date: 2004-08-11
New Economics Papers: this item is included in nep-ecm and nep-ets
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Working Paper: Bandwidth Selection for Multivariate Kernel Density Estimation Using MCMC (2004)
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Persistent link: https://EconPapers.repec.org/RePEc:ecm:ausm04:120

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