000162932 001__ 162932
000162932 005__ 20251017144629.0
000162932 0247_ $$2doi$$a10.1007/s11749-025-00984-8
000162932 0248_ $$2sideral$$a145452
000162932 037__ $$aART-2025-145452
000162932 041__ $$aeng
000162932 100__ $$0(orcid)0000-0001-8331-5160$$aAdell, José A.$$uUniversidad de Zaragoza
000162932 245__ $$aRandom positive linear operators and their applications to nonparametric statistics
000162932 260__ $$c2025
000162932 5060_ $$aAccess copy available to the general public$$fUnrestricted
000162932 5203_ $$aWe 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.
000162932 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E48-23R$$9info:eu-repo/grantAgreement/ES/DGA/S41-23R$$9info:eu-repo/grantAgreement/ES/MINECO-FEDER/PID2021-123737NB-I00
000162932 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttps://creativecommons.org/licenses/by/4.0/deed.es
000162932 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000162932 700__ $$0(orcid)0000-0001-7549-8825$$aAlcalá, J. T.$$uUniversidad de Zaragoza
000162932 700__ $$0(orcid)0000-0002-7099-7665$$aSangüesa, C.$$uUniversidad de Zaragoza
000162932 7102_ $$12007$$2265$$aUniversidad de Zaragoza$$bDpto. Métodos Estadísticos$$cÁrea Estadís. Investig. Opera.
000162932 773__ $$g(2025), [31 pp.]$$pTest (Madrid)$$tTest$$x1133-0686
000162932 8564_ $$s835060$$uhttps://zaguan.unizar.es/record/162932/files/texto_completo.pdf$$yVersión publicada
000162932 8564_ $$s1154607$$uhttps://zaguan.unizar.es/record/162932/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000162932 909CO $$ooai:zaguan.unizar.es:162932$$particulos$$pdriver
000162932 951__ $$a2025-10-17-14:25:23
000162932 980__ $$aARTICLE