Random positive linear operators and their applications to nonparametric statistics

Adell, José A. (Universidad de Zaragoza) ; Alcalá, J. T. (Universidad de Zaragoza) ; Sangüesa, C. (Universidad de Zaragoza)

Resumen: 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.

Idioma: Inglés

DOI: 10.1007/s11749-025-00984-8

Año: 2025

Publicado en: Test (2025), [31 pp.]
ISSN: 1133-0686

Financiación: info:eu-repo/grantAgreement/ES/DGA/E48-23R
Financiación: info:eu-repo/grantAgreement/ES/DGA/S41-23R
Financiación: info:eu-repo/grantAgreement/ES/MINECO-FEDER/PID2021-123737NB-I00

Tipo y forma: Article (Published version)

Área (Departamento): Área Estadís. Investig. Opera. (Dpto. Métodos Estadísticos)