Bayesian bandwidth selection in discrete multivariate associated kernel estimators for probability mass functions

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• 作者：Nawal Belaid^a ; ^{belaidnawelro@hotmail.fr" class="auth_mail" title="E-mail the corresponding author} ; Smail Adjabi^a ; ^{adjabi@hotmail.com" class="auth_mail" title="E-mail the corresponding author} ; Nabil Zougab^a ; ^b ; ^{nabilzougab@yahoo.fr" class="auth_mail" title="E-mail the corresponding author} ; C&eacute ; lestin C. Kokonendji^c ; ^{celestin.kokonendji@univ-fcomte.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 62G07 ; secondary ; 62G99
• 刊名：Journal of the Korean Statistical Society
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：45
• 期：4
• 页码：557-567
• 全文大小：493 K

文摘

This paper proposed a nonparametric estimator for probability mass function of multivariate data. The estimator is based on discrete multivariate associated kernel without correlation structure. For the choice of the bandwidth diagonal matrix, we presented the Bayes global method against the likelihood cross-validation one, and we used the Bayesian Markov chain Monte Carlo (MCMC) method for deriving the global optimal bandwidth. We have compared the proposed method with the cross-validation method. The performance of both methods is evaluated under the integrated square error criterion through simulation studies based on for univariate and multivariate models. We also presented applications of the proposed methods to bivariate and trivariate real data. The obtained results show that the Bayes global method performs better than cross-validation one, even for the Poisson kernel which is the very bad discrete associated kernel among binomial, discrete triangular and Dirac discrete uniform kernels.