Bayesian nonparametric estimation of bandwidth using mixtures of kernel estimators for length-biased data

Kernel density estimation has been applied in many computational subjects. In this paper, we propose a density estimation procedure from a Bayesian nonparametric perspective using Dirichlet process prior for the length-biased data under an unknown kernel function. In this situation, the kernel within the Dirichlet process mixture model will be approximated by the kernel density estimator. We present a Bayesian nonparametric method for finding the bandwidth parameter in the kernel density estimation using a Markov chain Monte Carlo approach. Then, this approach is used to the simulated and real data set. Finally, we compare the proposed bandwidth estimation with the other estimations like cross-validation and Bayes based on the mean integrated squared error criterion.