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MCMC method bandwidth selection for multivariate kernel density estimation

Kernel density estimation for multivariate data is an important
technique that has a wide range of applications in econometrics and
finance. The lower level of its use 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.
Numerical studies for five dimensional data show that our algorithm is
superior to the normal reference rule.

MCMC method bandwidth selection for multivariate kernel density

Session Nonparametric Estimation II
Field Econometrics
Session Chair Qi Li, Texas A&M University

Presenter(s) Maxwell King, Monash University
Co-Author(s) Xibin Zhang, Department of Econometrics and Business
Statistics, Monash University and Rob Hyndman, Monash University

Topics Semi/Nonparametrics
Keywords Cross-validation, Kullback-Leibler information, Mean
integrated squared errors, Monte Carlo kernel likelihood and Sampling

JEL Codes C11, C14, C51


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