A Bayesian Approach to Bandwidth Selection in Univariate Associate Kernel Estimation

Abstract

The fundamental problem in the associate kernel estimation of density or probability mass function (pmf) is the choice of the bandwidth. In this paper, we use a Bayesian approach based upon likelihood cross-validation and a Monte Carlo Markov chain (MCMC) method for deriving the global optimal bandwidth. A comparative simulation study of the MCMC method and the classical methods that adopt the asymptotic mean integrated square error () as criterion and the cross validation is presented for data generated from known densities and pmf, using standard AMISE and the practical integrated squared error. The simulation results show the superiority of the MCMC method over the classical methods.

Keywords:

• 62G07
• 62G90

Keywords:

• Cross validation
• likelihood
• MCMC method

Acknowledgments

We thank the anonymous referee and associate editor for their valuable comments.