Bayesian local bandwidth selector in multivariate associated kernel estimator for joint probability mass functions

ABSTRACT

This work treats non-parametric estimation of multivariate probability mass functions, using multivariate discrete associated kernels. We propose a Bayesian local approach to select the matrix of bandwidths considering the multivariate Dirac Discrete Uniform and the product of binomial kernels, and treating the bandwidths as a diagonal matrix of parameters with some prior distribution. The performances of this approach and the cross-validation method are compared using simulations and real count data sets. The obtained results show that the Bayes local method performs better than cross-validation in terms of integrated squared error.

KEYWORDS:

• Beta distribution
• binomial kernel
• cross-validation
• Dirac Discrete Uniform kernel

Acknowledgments

We sincerely thank an associate editor and the anonymous reviewers for their valuable comments.

Disclosure statement

No potential conflict of interest was reported by the authors.