This note concentrates on the nonparametric estimation of a probability mass function (p.m.f.) using discrete associated kernels. An expression of the optimal bandwidth minimizing the asymptotic part of the global squared error is given. Some asymptotic expressions of bias and variance of the cross-validation criterion are also presented. At last, the two bandwidth selection procedures are illustrated through some simulations and an application on a real count data set.
Cette note se focalise sur l'estimation non paramétrique à noyau associé discret d'une fonction de masse de probabilité. Une expression de la fenêtre optimale minimisant la partie asymptotique de l'erreur quadratique globale est donnée. Des expressions asymptotiques pour le biais et la variance d'un critère de sélection par validation croisée sont également présentées. Enfin, les deux méthodes de choix de fenêtre sont illustrées par des simulations et une application sur des données réelles.
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Tristan Senga Kiessé 1
@article{CRMATH_2016__354_7_735_0, author = {Tristan Senga Kiess\'e}, title = {On bandwidth parameter choices for discrete nonparametric kernel estimator}, journal = {Comptes Rendus. Math\'ematique}, pages = {735--740}, publisher = {Elsevier}, volume = {354}, number = {7}, year = {2016}, doi = {10.1016/j.crma.2016.02.012}, language = {en}, }
Tristan Senga Kiessé. On bandwidth parameter choices for discrete nonparametric kernel estimator. Comptes Rendus. Mathématique, Volume 354 (2016) no. 7, pp. 735-740. doi : 10.1016/j.crma.2016.02.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.02.012/
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