Bayesian Approach in Nonparametric Count Regression with Binomial Kernel

Recently, Kokonendji etal. have adapted the well-known Nadaraya-Watson kernel estimator for estimating the count function m in the context of nonparametric discrete regression. The authors have also investigated the bandwidth selection using the cross-validation method. In this article, we propose a Bayesian approach in the context of nonparametric count regression for estimating the bandwidth and the variance of the model error, which has not been estimated in Kokonendji etal. The model error is considered as Gaussian with mean of zero and a variance of sigma(2). The Bayes estimates cannot be obtained in closed form and then, we use the well-known Markov chain Monte Carlo (MCMC) technique to compute the Bayes estimates under the squared errors loss function. The performance of this proposed approach and the cross-validation method are compared through simulation and real count data.