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A Bayesian Approach to Bandwidth Selection in Univariate Associate Kernel Estimation

  • Nabil Zougab
  • Smail Adjabi
  • Célestin C. Kokonendji
Article

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 (AMISE) 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

Cross validation likelihood MCMC method 

AMS Subject Classification

62G07 62G90 

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Copyright information

© Grace Scientific Publishing 2013

Authors and Affiliations

  • Nabil Zougab
    • 1
  • Smail Adjabi
    • 1
  • Célestin C. Kokonendji
    • 2
  1. 1.LAMOS LaboratoryUniversity of BejaiaBejaiaAlgeria
  2. 2.LMB UMR 6623 CNRSUniversity of Franche-ComtéBesançon CedexFrance

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