162932 20251017144629.0 doi 10.1007/s11749-025-00984-8 sideral 145452 ART-2025-145452 eng Adell, José A. Universidad de Zaragoza (orcid)0000-0001-8331-5160 Random positive linear operators and their applications to nonparametric statistics 2025 Access copy available to the general public Unrestricted We outline a general procedure on how to apply random positive linear operators in nonparametric estimation. As a consequence, we give explicit confidence bands and intervals for a distribution function F concentrated on [0, 1] by means of random Bernstein polynomials, and for the derivatives of F by using random Bernstein–Kantorovich-type operators. In each case, the lengths of such bands and intervals depend upon the degree of smoothness of F or its corresponding derivatives, measured in terms of appropriate moduli of smoothness. In particular, we estimate the uniform distribution function by means of a random polynomial of second order. This estimator is much simpler and performs better than the classical uniform empirical process used in the celebrated Dvoretzky–Kiefer–Wolfowitz inequality. info:eu-repo/grantAgreement/ES/DGA/E48-23R info:eu-repo/grantAgreement/ES/DGA/S41-23R info:eu-repo/grantAgreement/ES/MINECO-FEDER/PID2021-123737NB-I00 info:eu-repo/semantics/openAccess by https://creativecommons.org/licenses/by/4.0/deed.es info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Alcalá, J. T. Universidad de Zaragoza (orcid)0000-0001-7549-8825 Sangüesa, C. Universidad de Zaragoza (orcid)0000-0002-7099-7665 2007 265 Universidad de Zaragoza Dpto. Métodos Estadísticos Área Estadís. Investig. Opera. (2025), [31 pp.] Test (Madrid) Test 1133-0686 835060 http://zaguan.unizar.es/record/162932/files/texto_completo.pdf Versión publicada 1154607 http://zaguan.unizar.es/record/162932/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:162932 articulos driver 2025-10-17-14:25:23 ARTICLE