Bayesian bandwidth selection with two multiplicative bias correction estimators for discrete kernel

Abstract

–Two classes of multiplicative bias correction (MBC) methods with discrete associated kernels are used for probability mass function estimation. The MBC estimators reduce the order of magnitude in bias, whereas the order of magnitude in variance remains unchanged. For the choice of the bandwidth, we proposed the Bayes global method against the unbiased cross-validation approach. The performance of both methods (Bayesian and cross validation methods) are evaluated under two criteria: the integrated square error criteria and the integrated square bias through simulation studies. We also present a real data application of the proposed methods. The obtained results show that the Bayes global method performs better than cross-validation one for MBC estimators.