Bayesian adaptive bandwidth selector for multivariate discrete kernel estimator

ABSTRACT

We treat a non parametric estimator for joint probability mass function, based on multivariate discrete associated kernels which are appropriated for multivariate count data of small and moderate sample sizes. Bayesian adaptive estimation of the vector of bandwidths using the quadratic and entropy loss functions is considered. Exact formulas for the posterior distribution and the vector of bandwidths are obtained. Numerical studies indicate that the performance of our approach is better, comparing with other bandwidth selection techniques using integrated squared error as criterion. Some applications are made on real data sets.

KEYWORDS:

• Binomial kernel
• cross-validation
• non parametric estimator
• product of kernels

Acknowledgments

Part of this work was done while the first author was at Laboratoire de Mathématiques de Besançon as a visiting scientist, with the support of the University of Bejaia by the Research Unit LaMOS. We sincerely thank the associate editor and the anonymous reviewers for their valuable comments.