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

• Published in: Journal of statistical computation and simulation Vol. 90; no. 10; pp. 1849 - 1874
• Main Authors: Rahnamay Kordasiabi, S., Khazaei, S.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 02.07.2020; Taylor & Francis Ltd
• Subjects: bandwidth selection; Bandwidths; Bayesian analysis; Bayesian nonparametric; Computer simulation; Density; Dirichlet problem; Dirichlet process prior; kernel estimator; Kernel functions; Length-biased data analysis; Markov analysis; Markov chains; Nonparametric statistics; Parameter estimation; pivoting method
• ISSN: 0094-9655; 1563-5163
• DOI: 10.1080/00949655.2020.1750613

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.