Bayesian adaptive bandwidth selector for multivariate discrete kernel estimator |
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Authors: | Nawal Belaid Smail Adjabi Célestin C Kokonendji Nabil Zougab |
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Institution: | 1. Research Unit LaMOS, University of Bejaia, Bejaia, Algeriabelaidnawelro@hotmail.fr;3. Research Unit LaMOS, University of Bejaia, Bejaia, Algeria;4. Bourgogne Franche-Comté University, LMB UMR 6623 CNRS-UFC, Besan?on Cedex, France |
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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. |
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Keywords: | Binomial kernel cross-validation non parametric estimator product of kernels |
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