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| Titre: | Stochastic Bernstein polynomials: uniform convergence in probability with rates |
| Auteur(s): | Adell, José A. Cárdenas-Morales, Daniel |
| Résumé: | We introduce stochastic variants of the classical Bernstein polynomials associated with a continuous function f , built up from a general triangular array of random variables. We discuss the uniform convergence in probability of the approximation process that they represent, providing at the same time rates of convergence. In the particular case in which the triangular array of random variables consists of the uniform order statistics, we give a positive answer to a conjectured raised in Wu and Zhou (Adv. Comput. Math. 46, 8, 2020) about an exponential rate of convergence in probability. |
| Mots-clés: | Stochastic Bernstein polynomials Uniform convergence in probability Rates of convergence Confidence band Bernstein-Durrmeyer polynomials |
| Date de publication: | 27-fév-2020 |
| metadata.dc.description.sponsorship: | This work is partially supported by the Spanish government Research Project PGC2018-097621-B-I00. The second author is also supported by Junta de Andalucía Research Group FQM-0178. |
| Editeur: | Springer |
| Référence bibliographique: | Adell, J.A., Cárdenas-Morales, D. Stochastic Bernstein polynomials: uniform convergence in probability with rates. Adv Comput Math 46, 16 (2020). |
| Collection(s) : | DM-Artículos |
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