Binomial kernel and Bayes local bandwidth in discrete function estimation

Abstract

The Bayesian approach to bandwidth selection in discrete associated kernel estimation of probability mass function is a very good alternative to the classical popular methods such as the methods which adopt the asymptotic mean integrated squared error as a criterion and the cross-validation technique. In this paper, we propose a Bayesian local approach to bandwidth selection considering the binomial kernel estimator and locally treating the bandwidth h as a random quantity with a prior distribution. The local bandwidth is estimated by the posterior mean of h. The performance of this proposed approach and that of the classical methods are compared using simulations of data generated from known discrete functions. The new method is then applied to a real count data set. The smoothing quality of the Bayes estimator is very satisfactory.

Keywords:

• cross-validation
• discrete associated kernel
• prior distribution

AMS Subject Classification :

• 62G07
• 62G99

Acknowledgements

We sincerely thank an associate editor and two anonymous referees for their valuable comments.