Comparison study to bandwidth selection in binomial kernel estimation using Bayesian approaches

Recently, several works have shown that the Bayesian approaches to global bandwidth and variable (local and adaptive) bandwidths selection in binomial kernel estimation for probability mass functions (pmfs) outperform the common classical methods, such as mean integrated squared error (MISE) and cross-validation (CV) methods. In this article, we first review the global, local, and adaptive binomial kernel estimator combined with the Bayesian approaches for selecting the bandwidths. Then we compare them by using several count data sets with different designs, in particular for small and moderate sample sizes. All the Bayesian bandwidth selection approaches are also applied to a real count data sets. In general, in terms of integrated squared error (ISE) and execution times, the local Bayesian approach outperforms the other Bayesian approaches.